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## Lagarias, Jeffrey C.

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 Author ID: lagarias.jeffrey-c Published as: Lagarias, Jeffrey C.; Lagarias, J. C.; Lagarias, Jeffrey; Lagarias, J. Homepage: http://www.math.lsa.umich.edu/~lagarias/ External Links: MGP · Wikidata · ORCID · dblp · GND
 Documents Indexed: 224 Publications since 1977, including 3 Books Reviewing Activity: 3 Reviews
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#### Co-Authors

 61 single-authored 14 Odlyzko, Andrew M. 13 Wang, Yang 7 Håstad, Johan Torkel 6 Fishburn, Peter Clingerman 6 Flatto, Leopold 6 Rains, Eric M. 6 Reeds, James A. 5 Abram, William C. 5 Daubechies, Ingrid Chantal 5 Mallows, Colin Lingwood 5 Wilks, Allan R. 4 Graham, Ronald Lewis 4 Hass, Joel 4 Kahn, Jeff D. 4 Li, Wen-Ch’ing Winnie 4 Schnorr, Claus Peter 4 Witsenhausen, Hans S. 4 Yan, Catherine Huafei 3 Bayer, David Allen 3 Coffman, Edward Grady jun. 3 Kurlberg, Pär 3 Pomerance, Carl Bernard 3 Richman, David Harry 3 Shearer, James B. 3 Shor, Peter Williston 3 Soundararajan, Kannan 2 Bell, Jason P. 2 Boppana, Ravi B. 2 Cohn, Harvey 2 Just, Bettina 2 Maddock, Zachary 2 Mehta, Harsh 2 Pleasants, Peter A. B. 2 Pollington, Andrew Douglas 2 Poonen, Bjorn 2 Porta, Horacio A. 2 Rhoades, Robert C. 2 Richardson, Thomas J. 2 Shallit, Jeffrey O. 2 Shepp, Lawrence Alan 2 Sloane, Neil James Alexander 2 Stolarsky, Kenneth B. 2 Vanderbei, Robert Joseph 2 Wright, Margaret H. 2 Wright, Paul E. 1 Adams, Fred C. 1 Aminzadeh, Fred 1 Andersen, Nickolas 1 Baker, Brenda S. 1 Bernstein, Daniel Julius 1 Bloch, Anthony M. 1 Bolshakov, Artem 1 Bombieri, Enrico 1 Bruno, John L. 1 Calderbank, Arthur Robert 1 Conway, John Horton 1 Dolbilin, Nikolaĭ Petrovich 1 Doyle, Peter G. 1 Eriksson, Nicholas 1 Feigenbaum, Joan 1 Frankl, Péter 1 Freed, Daniel Stuart 1 Friedlander, John Benjamin 1 Frieze, Alan Michael 1 Furedi, Zoltan 1 Gehrlein, William V. 1 Geoghegan, Ross 1 Gopinath, B. 1 Grabiner, David J. 1 Griggs, Jerrold R. 1 Güntürk, Cemalettin Sinan 1 Helfrich, Bettina 1 Hwang, Frank Kwangming 1 Hyde, Trevor 1 Kannan, Ravindran 1 Karmarkar, Narendra K. 1 Kim, Jeong Han 1 Kolountzakis, Mihail N. 1 Kontorovich, Alex V. 1 Krasikov, Ilia 1 Kusner, Rob 1 Kusner, Wöden 1 Lenstra, Hendrik W. jun. 1 Luo, Yusheng 1 Melville, Robert C. 1 Miller, Victor S. 1 Moews, David 1 Montague, David 1 Montgomery, Hugh Lowell 1 Morgan, Frank 1 Murayama, Takumi 1 Neshveyev, Sergey V. 1 Padrol, Arnau 1 Pippenger, Nicholas J. 1 Rodgers, Brad 1 Romano, D. S. 1 Senechal, Marjorie Wikler 1 Shamir, Adi 1 Shlosman, Senya B. 1 Slonim, Daniel J. ...and 16 more Co-Authors
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#### Serials

 13 Discrete & Computational Geometry 11 Journal of Number Theory 10 Acta Arithmetica 7 American Mathematical Monthly 6 SIAM Journal on Computing 6 Transactions of the American Mathematical Society 6 Experimental Mathematics 5 Mathematics of Computation 5 Ergodic Theory and Dynamical Systems 4 Journal of Combinatorial Theory. Series A 4 Journal of the London Mathematical Society. Second Series 4 Linear Algebra and its Applications 4 SIAM Journal on Optimization 4 The Journal of Fourier Analysis and Applications 3 Discrete Mathematics 3 Canadian Journal of Mathematics 3 Journal für die Reine und Angewandte Mathematik 3 Monatshefte für Mathematik 3 Pacific Journal of Mathematics 3 SIAM Journal on Discrete Mathematics 3 Forum Mathematicum 3 Bulletin of the American Mathematical Society. New Series 3 Journal de Théorie des Nombres de Bordeaux 3 Journal of Difference Equations and Applications 2 Annales de l’Institut Fourier 2 Duke Mathematical Journal 2 Illinois Journal of Mathematics 2 Inventiones Mathematicae 2 Mathematics of Operations Research 2 Proceedings of the London Mathematical Society. Third Series 2 Journal of Algorithms 2 Advances in Applied Mathematics 2 SIAM Journal on Algebraic and Discrete Methods 2 IMRN. International Mathematics Research Notices 2 Journal of the Australian Mathematical Society. Series A 2 SIAM Journal on Mathematical Analysis 2 The Ramanujan Journal 2 International Journal of Number Theory 2 Journal of Fractal Geometry 2 Research in the Mathematical Sciences 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 IEEE Transactions on Information Theory 1 Information Processing Letters 1 Nonlinearity 1 Reviews in Mathematical Physics 1 Advances in Mathematics 1 Applied Mathematics and Optimization 1 Canadian Mathematical Bulletin 1 Commentarii Mathematici Universitatis Sancti Pauli 1 The Fibonacci Quarterly 1 Geometriae Dedicata 1 Indiana University Mathematics Journal 1 International Journal of Game Theory 1 Journal of the Association for Computing Machinery 1 Journal of Differential Geometry 1 Journal of Functional Analysis 1 Mathematische Annalen 1 European Journal of Combinatorics 1 Combinatorica 1 Order 1 Algorithmica 1 AT&T Technical Journal 1 Information and Computation 1 Journal of the American Mathematical Society 1 SIAM Journal on Matrix Analysis and Applications 1 The Annals of Applied Probability 1 Bulletin of the Institute of Mathematics. Academia Sinica 1 L’Enseignement Mathématique. 2e Série 1 SIAM Journal on Applied Mathematics 1 Notices of the American Mathematical Society 1 Computer Networks and ISDN Systems 1 Mathematical Programming. Series A. Series B 1 Journal of the ACM 1 The Quarterly Journal of Mathematics 1 Integers 1 Contemporary Mathematics 1 Communications in Number Theory and Physics 1 RIMS Kôkyûroku Bessatsu 1 Arnold Mathematical Journal 1 Research in Number Theory
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#### Fields

 126 Number theory (11-XX) 40 Convex and discrete geometry (52-XX) 36 Dynamical systems and ergodic theory (37-XX) 26 Computer science (68-XX) 21 Combinatorics (05-XX) 16 Operations research, mathematical programming (90-XX) 15 Information and communication theory, circuits (94-XX) 13 Measure and integration (28-XX) 12 Harmonic analysis on Euclidean spaces (42-XX) 11 Real functions (26-XX) 11 Numerical analysis (65-XX) 10 Probability theory and stochastic processes (60-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Group theory and generalizations (20-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Ordinary differential equations (34-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 6 Geometry (51-XX) 5 Operator theory (47-XX) 5 General topology (54-XX) 4 Field theory and polynomials (12-XX) 4 Difference and functional equations (39-XX) 4 Differential geometry (53-XX) 4 Manifolds and cell complexes (57-XX) 3 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 3 Functions of a complex variable (30-XX) 3 Functional analysis (46-XX) 2 Mathematical logic and foundations (03-XX) 2 Algebraic geometry (14-XX) 2 Approximations and expansions (41-XX) 2 Integral transforms, operational calculus (44-XX) 2 Mechanics of particles and systems (70-XX) 2 Systems theory; control (93-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Category theory; homological algebra (18-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX)

#### Citations contained in zbMATH Open

193 Publications have been cited 3,400 times in 2,488 Documents Cited by Year
Convergence properties of the Nelder–Mead simplex method in low dimensions. Zbl 1005.90056
Lagarias, Jeffrey C.; Reeds, James A.; Wright, Margaret H.; Wright, Paul E.
1998
Two-scale difference equations. II: Local regularity, infinite products of matrices, and fractals. Zbl 0788.42013
Daubechies, Ingrid; Lagarias, Jeffrey C.
1992
Sets of matrices all infinite products of which converge. Zbl 0746.15015
Daubechies, Ingrid; Lagarias, Jeffrey C.
1992
Two-scale difference equations. I: Existence and global regularity of solutions. Zbl 0763.42018
Daubechies, Ingrid; Lagarias, Jeffrey C.
1991
Self-affine tiles in $$\mathbb{R}^n$$. Zbl 0893.52013
Lagarias, Jeffrey C.; Wang, Yang
1996
Effective versions of the Chebotarev density theorem. Zbl 0362.12011
Lagarias, J. C.; Odlyzko, A. M.
1977
The $$3x+1$$ problem and its generalizations. Zbl 0566.10007
Lagarias, Jeffrey C.
1985
Integral self-affine tiles in $$\mathbb{R}^n$$. II: Lattice tilings. Zbl 0893.52015
Lagarias, Jeffrey C.; Wang, Yang
1997
The finiteness conjecture for the generalized spectral radius of a set of matrices. Zbl 0818.15007
Lagarias, Jeffrey C.; Wang, Yang
1995
Integral self-affine tiles in $$\mathbb{R}^n$$. I: Standard and nonstandard digit sets. Zbl 0893.52014
Lagarias, Jeffrey C.; Wang, Yang
1996
The nonlinear geometry of linear programming. I: Affine and projective scaling trajectories. Zbl 0671.90045
Bayer, D. A.; Lagarias, J. C.
1989
Tiling the line with translates of one tile. Zbl 0847.05037
Lagarias, Jeffrey C.; Wang, Yang
1996
Bounds for lattice polytopes containing a fixed number of interior points in a sublattice. Zbl 0752.52010
Lagarias, Jeffrey C.; Ziegler, Günter M.
1991
Repetitive Delone sets and quasicrystals. Zbl 1062.52021
Lagarias, Jeffrey C.; Pleasants, Peter A. B.
2003
Tiling with polyominoes and combinatorial group theory. Zbl 0741.05019
Conway, J. H.; Lagarias, J. C.
1990
A bound for the least prime ideal in the Chebotarev density theorem. Zbl 0401.12014
Lagarias, J. C.; Montgomery, H. L.; Odlyzko, A. M.
1979
Complements to Li’s criterion for the Riemann Hypothesis. Zbl 0972.11079
Bombieri, Enrico; Lagarias, Jeffrey C.
1999
Euler’s constant: Euler’s work and modern developments. Zbl 1282.11002
Lagarias, Jeffrey C.
2013
The nonlinear geometry of linear programming. II: Legendre transform coordinates and central trajectories. Zbl 0671.90046
Bayer, D. A.; Lagarias, J. C.
1989
Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice. Zbl 0723.11029
Lagarias, J. C.; Lenstra, H. W. jun.; Schnorr, C. P.
1990
The computational complexity of simultaneous diophantine approximation problems. Zbl 0563.10025
Lagarias, J. C.
1985
Solving low-density subset sum problems. Zbl 0632.94007
Lagarias, J. C.; Odlyzko, A. M.
1985
The computational complexity of knot and link problems. Zbl 1065.68667
Hass, Joel; Lagarias, Jeffrey C.; Pippenger, Nicholas
1999
Orthonormal bases of exponentials for the $$n$$-cube. Zbl 0978.42007
Lagarias, Jeffrey C.; Reeds, James A.; Wang, Yang
2000
Mathematical quasicrystals and the problem of diffraction. Zbl 1161.52312
Lagarias, Jeffrey C.
2000
Spectral sets and factorizations of finite abelian groups. Zbl 0898.47002
Lagarias, Jeffrey C.; Wang, Yang
1997
Apollonian circle packings: Number theory. Zbl 1026.11058
Graham, Ronald L.; Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R.; Yan, Catherine H.
2003
Geometric models for quasicrystals. I. Delone sets of finite type. Zbl 0924.68190
Lagarias, J. C.
1999
Meyer’s concept of quasicrystal and quasiregular sets. Zbl 0858.52010
Lagarias, J. C.
1996
Keller’s cube-tiling conjecture is false in high dimensions. Zbl 0759.52013
Lagarias, Jeffrey C.; Shor, Peter W.
1992
Haar type orthonormal wavelet bases in $$R^2$$. Zbl 0908.42022
Lagarias, Jeffrey C.; Wang, Yang
1995
Sets uniquely determined by projections on axes. II: Discrete case. Zbl 0752.44002
Fishburn, P. C.; Lagarias, J. C.; Reeds, J. A.; Shepp, L. A.
1991
Geodesic multidimensional continued fractions. Zbl 0813.11040
Lagarias, J. C.
1994
Haar bases for $$L^ 2 (\mathbb{R}^ n)$$ and algebraic number theory. Zbl 0886.11062
Lagarias, Jeffrey C.; Wang, Yang
1996
The number of Reidemeister moves needed for unknotting. Zbl 0964.57005
Hass, Joel; Lagarias, Jeffrey C.
2001
Apollonian circle packings: Geometry and group theory. I: The Apollonian group. Zbl 1085.52010
Graham, Ronald L.; Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R.; Yan, Catherine H.
2005
The Takagi function and its properties. Zbl 1275.26011
Lagarias, Jeffrey C.
2012
Structure of tilings of the line by a function. Zbl 0854.58016
Kolountzakis, Mihail N.; Lagarias, Jeffrey C.
1996
Polynomial time algorithms for finding integer relations among real numbers. Zbl 0692.10033
Håstad, Johan; Just, B.; Lagarias, J. C.; Schnorr, C. P.
1989
Corrigendum/addendum to: Sets of matrices all infinite products of which converge. Zbl 0978.15024
Daubechies, Ingrid; Lagarias, Jeffrey C.
2001
I.I. Dikin’s convergence result for the affine-scaling algorithm. Zbl 0727.90050
Vanderbei, R. J.; Lagarias, J. C.
1990
Substitution Delone sets. Zbl 1037.52017
Lagarias, Jeffrey C.; Wang, Yang
2003
Reconstructing truncated integer variables satisfying linear congruences. Zbl 0654.10006
Frieze, Alan M.; Håstad, Johan; Kannan, Ravi; Lagarias, Jeffrey C.; Shamir, Adi
1988
On the thermodynamic formalism for multifractal functions. Zbl 0843.58091
Daubechies, Ingrid; Lagarias, Jeffrey C.
1994
The quality of the diophantine approximations found by the Jacobi–Perron algorithm and related algorithms. Zbl 0790.11059
Lagarias, J. C.
1993
Best simultaneous Diophantine approximations. I: Growth rates of best approximation denominators. Zbl 0495.10021
Lagarias, J. C.
1982
Best simultaneous Diophantine approximations. II: Behavior of consecutive best approximations. Zbl 0497.10025
Lagarias, J. C.
1982
On the computational complexity of determining the solvability or unsolvability of the equation $$X^2-DY^2=-1$$. Zbl 0446.10014
Lagarias, J. C.
1980
Beyond the Descartes circle theorem. Zbl 1027.51022
Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R.
2002
An elementary problem equivalent to the Riemann hypothesis. Zbl 1098.11005
Lagarias, Jeffrey C.
2002
Pseudorandom number generators in cryptography and number theory. Zbl 0747.94011
Lagarias, J. C.
1990
Li coefficients for automorphic $$L$$-functions. Zbl 1216.11078
Lagarias, Jeffrey
2007
On the range of fractional parts $$\{\xi(p/q)^ n\}$$. Zbl 0821.11038
Flatto, Leopold; Lagarias, Jeffrey C.; Pollington, Andrew D.
1995
The zeta function of the beta transformation. Zbl 0843.58106
Flatto, Leopold; Lagarias, Jeffrey C.; Poonen, Bjorn
1994
Apollonian circle packings: Geometry and group theory. III: Higher dimensions. Zbl 1085.52012
Graham, Ronald L.; Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R.; Yan, Catherine H.
2006
Worst-case complexity bounds for algorithms in the theory of integral quadratic forms. Zbl 0473.68030
Lagarias, J. C.
1980
The nonlinear geometry of linear programming. III: Projective Legendre transform coordinates and Hilbert geometry. Zbl 0699.90070
Lagarias, J. C.
1990
Computing $$\pi(x)$$: an analytic method. Zbl 0622.10027
Lagarias, J. C.; Odlyzko, A. M.
1987
Number theory and dynamical systems. Zbl 0773.11051
Lagarias, J. C.
1992
The ultimate challenge. The $$3x+1$$ problem. Zbl 1253.11003
Lagarias, Jeffrey C. (ed.)
2010
Computing $$\pi(x)$$: the Meissel-Lehmer method. Zbl 0564.10006
Lagarias, J. C.; Miller, V. S.; Odlyzko, A. M.
1985
The set of primes dividing the Lucas numbers has density 2/3. Zbl 0569.10003
Lagarias, J. C.
1985
Karmarkar’s linear programming algorithm and Newton’s method. Zbl 0736.90053
Bayer, D. A.; Lagarias, J. C.
1991
Apollonian circle packings: Geometry and group theory. II: Super-Apollonian group and integral packings. Zbl 1085.52011
Graham, Ronald L.; Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R.; Yan, Catherine H.
2006
Self-packing of centrally symmetric convex bodies in $$\mathbb{R}{}^ 2$$. Zbl 0756.52016
Doyle, P. G.; Lagarias, J. C.; Randall, D.
1992
On computing Artin L-functions in the critical strip. Zbl 0409.12017
Lagarias, J. C.; Odlyzko, A. M.
1979
Local complexity of Delone sets and crystallinity. Zbl 1016.52013
Lagarias, Jeffrey C.; Pleasants, Peter A. B.
2002
Corrigendum/Addendum: Haar bases for $$L^2 (\mathbb{R}^n)$$ and algebraic number theory. Zbl 1007.11066
Lagarias, Jeffrey C.; Wang, Yang
1999
Multiregular point systems. Zbl 0915.51017
Dolbilin, N. P.; Lagarias, J. C.; Senechal, M.
1998
The set of rational cycles for the $$3x+1$$ problem. Zbl 0773.11017
Lagarias, Jeffrey C.
1990
The $$3x +1$$ problem: Two stochastic models. Zbl 0742.60027
Lagarias, J. C.; Weiss, A.
1992
Power series variants of Karmarkar-type algorithms. Zbl 0682.90060
Karmarkar, Narendra K.; Lagarias, Jeffrey C.; Slutsman, Lev; Wang, Pyng
1989
Hilbert spaces of entire functions and Dirichlet $$L$$-functions. 2nd printing. Zbl 1121.11057
Lagarias, Jeffrey C.
2006
Cube-tilings of $$\mathbb{R}^ n$$ and nonlinear codes. Zbl 0804.52013
Lagarias, J. C.; Shor, P. W.
1994
Orthogonality criteria for compactly supported refinable functions and refinable function vectors. Zbl 0952.42017
Lagarias, Jeffrey C.; Wang, Yang
2000
The Lerch zeta function. I: Zeta integrals. Zbl 1253.11085
Lagarias, Jeffrey C.; Li, Wen-Ching Winnie
2012
The Lerch zeta function. II: Analytic continuation. Zbl 1253.11086
Lagarias, Jeffrey C.; Li, Wen-Ching Winnie
2012
The Riemann hypothesis for certain integrals of Eisenstein series. Zbl 1208.11106
Lagarias, Jeffrey C.; Suzuki, Masatoshi
2006
Ternary expansions of powers of 2. Zbl 1193.11008
Lagarias, Jeffrey C.
2009
Dynamics of a family of piecewise-linear area-preserving plane maps. I. Rational rotation numbers. Zbl 1082.37044
Lagarias, Jeffrey C.; Rains, Eric
2005
Sets uniquely determined by projections on axes. I: Continuous case. Zbl 0695.44003
Fishburn, P. C.; Lagarias, J. C.; Reeds, J. A.; Shepp, L. A.
1990
Geometric models for quasicrystals. II. Local rules under isometries. Zbl 0930.51019
Lagarias, J. C.
1999
Universal spectra and Tijdeman’s conjecture on factorization of cyclic groups. Zbl 0988.47006
Lagarias, Jeffrey C.; Szabó, Sándor
2001
Zero spacing distributions for differenced $$L$$-functions. Zbl 1120.11037
Lagarias, Jeffrey C.
2005
Benford’s law for the $$3x+1$$ function. Zbl 1117.11018
Lagarias, Jeffrey C.; Soundararajan, K.
2006
Level sets of the Takagi function: generic level sets. Zbl 1263.26020
2011
Approximation algorithms for maximizing the number of squares packed into a rectangle. Zbl 0558.05002
Baker, B. S.; Calderbank, A. R.; Coffman, E. G. jun.; Lagarias, J. C.
1983
On the robustness of single-loop sigma-delta modulation. Zbl 1018.94520
Güntürk, C. Sinan; Lagarias, Jeffrey C.; Vaishampayan, Vinay A.
2001
Algorithms for packing squares: A probabilistic analysis. Zbl 0671.68014
Coffman, E. G. jun.; Lagarias, J. C.
1989
Mysteries in packing regular tetrahedra. Zbl 1284.52018
Lagarias, Jeffrey C.; Zong, Chuanming
2012
Asymmetric tent map expansions. I: Eventually periodic points. Zbl 0809.11041
Lagarias, J. C.; Porta, H. A.; Stolarsky, K. B.
1993
Counting smooth solutions to the equation $$A+B=C$$. Zbl 1270.11031
Lagarias, J. C.; Soundararajan, K.
2012
On the existence of fields governing the 2-invariants of the classgroup of $$Q(\sqrt{dp})$$ as p varies. Zbl 0523.12002
Cohn, Harvey; Lagarias, J. C.
1983
Probabilities for intersecting systems and random subsets of finite sets. Zbl 0582.60014
Fishburn, P. C.; Frankl, P.; Freed, D.; Lagarias, J. C.; Odlyzko, A. M.
1986
On the distribution in short intervals of integers having no large prime factor. Zbl 0606.10033
Friedlander, J. B.; Lagarias, J. C.
1987
The lap-counting function for linear mod one transformations. I: Explicit formulas and renormalizability. Zbl 0865.58016
Flatto, Leopold; Lagarias, Jeffrey C.
1996
Cutting sequences for geodesic flow on the modular surface and continued fractions. Zbl 1040.37008
Grabiner, David J.; Lagarias, Jeffrey C.
2001
On the density of sequences of integers the sum of no two of which is a square. II: General sequences. Zbl 0514.10041
Lagarias, J. C.; Odlyzko, A. M.; Shearer, J. B.
1983
Singularities of minimal surfaces and networks and related extremal problems in Minkowski space. Zbl 0762.49014
Füredi, Z.; Lagarias, J. C.; Morgan, F.
1991
Level sets of the Takagi function: local level sets. Zbl 1248.26008
2012
Dilated floor functions having nonnegative commutator. I: Positive and mixed sign dilations. Zbl 1454.11012
Lagarias, Jeffrey C.; Richman, David Harry
2019
Configuration spaces of equal spheres touching a given sphere: the twelve spheres problem. Zbl 1442.52015
Kusner, Rob; Kusner, Wöden; Lagarias, Jeffrey C.; Shlosman, Senya
2018
Shifted polyharmonic Maass forms for $$\text{PSL} (2,{\mathbb Z})$$. Zbl 1440.11078
Andersen, Nickolas; Lagarias, Jeffrey C.; Rhoades, Robert C.
2018
Intersections of multiplicative translates of 3-adic Cantor sets. II: Two infinite families. Zbl 1422.11163
Abram, William C.; Bolshakov, Artem; Lagarias, Jeffrey C.
2017
Products of Farey fractions. Zbl 1422.11167
Lagarias, Jeffrey C.; Mehta, Harsh
2017
The Lerch zeta function. III: Polylogarithms and special values. Zbl 1412.11110
Lagarias, Jeffrey C.; Li, Wen-Ching Winnie
2016
Polyharmonic Maass forms for $$\mathrm{PSL}(2,\mathbb Z)$$. Zbl 1418.11077
Lagarias, Jeffrey C.; Rhoades, Robert C.
2016
A family of measures on symmetric groups and the field with one element. Zbl 1337.11074
Lagarias, Jeffrey C.
2016
The Lerch zeta function. IV: Hecke operators. Zbl 1411.11081
Lagarias, Jeffrey C.; Li, Wen-Ching Winnie
2016
Dilated floor functions that commute. Zbl 1391.11008
Lagarias, Jeffrey C.; Murayama, Takumi; Richman, D. Harry
2016
Products of binomial coefficients and unreduced Farey fractions. Zbl 1360.11037
Lagarias, Jeffrey C.; Mehta, Harsh
2016
Splitting behavior of $$S_n$$-polynomials. Zbl 1378.11092
Lagarias, Jeffrey C.; Weiss, Benjamin L.
2015
A Skolem-Mahler-Lech theorem for iterated automorphisms of $$K$$-algebras. Zbl 1370.11048
Bell, Jason P.; Lagarias, Jeffrey C.
2015
$$p$$-adic path set fractals and arithmetic. Zbl 1291.11107
Abram, William C.; Lagarias, Jeffrey C.
2014
Path sets in one-sided symbolic dynamics. Zbl 1347.37027
Abram, William C.; Lagarias, Jeffrey C.
2014
Intersections of multiplicative translates of 3-adic Cantor sets. Zbl 1332.11074
Abram, William C.; Lagarias, Jeffrey C.
2014
Euler’s constant: Euler’s work and modern developments. Zbl 1282.11002
Lagarias, Jeffrey C.
2013
The Takagi function and its properties. Zbl 1275.26011
Lagarias, Jeffrey C.
2012
The Lerch zeta function. I: Zeta integrals. Zbl 1253.11085
Lagarias, Jeffrey C.; Li, Wen-Ching Winnie
2012
The Lerch zeta function. II: Analytic continuation. Zbl 1253.11086
Lagarias, Jeffrey C.; Li, Wen-Ching Winnie
2012
Mysteries in packing regular tetrahedra. Zbl 1284.52018
Lagarias, Jeffrey C.; Zong, Chuanming
2012
Counting smooth solutions to the equation $$A+B=C$$. Zbl 1270.11031
Lagarias, J. C.; Soundararajan, K.
2012
Level sets of the Takagi function: local level sets. Zbl 1248.26008
2012
Convergence of the restricted Nelder-Mead algorithm in two dimensions. Zbl 1246.49029
Lagarias, Jeffrey C.; Poonen, Bjorn; Wright, Margaret H.
2012
Product-free sets with high density. Zbl 1357.11028
Kurlberg, Pär; Lagarias, Jeffrey C.; Pomerance, Carl
2012
Level sets of the Takagi function: generic level sets. Zbl 1263.26020
2011
The Kepler conjecture. The Hales-Ferguson proof. Including a special issue of Discrete & Computational Geometry. Zbl 1234.52002
Lagarias, Jeffrey C.
2011
Smooth solutions to the $$abc$$ equation: the $$xyz$$ conjecture. Zbl 1270.11032
Lagarias, Jeffrey C.; Soundararajan, Kannan
2011
The integral of the Riemann $$\xi$$-function. Zbl 1270.11085
Lagarias, Jeffrey C.; Montague, David
2011
The ultimate challenge. The $$3x+1$$ problem. Zbl 1253.11003
Lagarias, Jeffrey C.
2010
Stochastic models for the $$3x+1$$ and $$5x+1$$ problems and related problems. Zbl 1253.11035
Kontorovich, Alex V.; Lagarias, Jeffrey C.
2010
Cyclic systems of simultaneous congruences. Zbl 1243.11050
Lagarias, Jeffrey C.
2010
The $$3x+1$$ problem: an overview. Zbl 1253.11036
Lagarias, Jeffrey C.
2010
The $$3x+1$$ problem and its generalizations. Zbl 1253.11037
Lagarias, Jeffrey C.
2010
Ternary expansions of powers of 2. Zbl 1193.11008
Lagarias, Jeffrey C.
2009
The Schrödinger operator with Morse potential on the right half-line. Zbl 1202.34149
Lagarias, Jeffrey C.
2009
Li coefficients for automorphic $$L$$-functions. Zbl 1216.11078
Lagarias, Jeffrey
2007
Apollonian circle packings: number theory. II: Spherical and hyperbolic packings. Zbl 1165.11057
Eriksson, Nicholas; Lagarias, Jeffrey C.
2007
Apollonian circle packings: Geometry and group theory. III: Higher dimensions. Zbl 1085.52012
Graham, Ronald L.; Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R.; Yan, Catherine H.
2006
Apollonian circle packings: Geometry and group theory. II: Super-Apollonian group and integral packings. Zbl 1085.52011
Graham, Ronald L.; Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R.; Yan, Catherine H.
2006
Hilbert spaces of entire functions and Dirichlet $$L$$-functions. 2nd printing. Zbl 1121.11057
Lagarias, Jeffrey C.
2006
The Riemann hypothesis for certain integrals of Eisenstein series. Zbl 1208.11106
Lagarias, Jeffrey C.; Suzuki, Masatoshi
2006
Benford’s law for the $$3x+1$$ function. Zbl 1117.11018
Lagarias, Jeffrey C.; Soundararajan, K.
2006
The $$3x+1$$ semigroup. Zbl 1163.11314
Applegate, David; Lagarias, Jeffrey C.
2006
The Riemann hypothesis: arithmetic and geometry. Zbl 1119.11051
Lagarias, Jeffrey C.
2006
Wild and Wooley numbers. Zbl 1232.11041
Lagarias, Jeffrey C.
2006
Apollonian circle packings: Geometry and group theory. I: The Apollonian group. Zbl 1085.52010
Graham, Ronald L.; Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R.; Yan, Catherine H.
2005
Dynamics of a family of piecewise-linear area-preserving plane maps. I. Rational rotation numbers. Zbl 1082.37044
Lagarias, Jeffrey C.; Rains, Eric
2005
Zero spacing distributions for differenced $$L$$-functions. Zbl 1120.11037
Lagarias, Jeffrey C.
2005
Dynamics of a family of piecewise-linear area-preserving plane maps II. Invariant circles. Zbl 1082.37045
Lagarias, Jeffrey C.; Rains, Eric
2005
Dynamics of a family of piecewise-linear area-preserving plane maps III. Cantor set spectra. Zbl 1082.37046
Lagarias, Jeffrey C.; Rains, Eric
2005
Area inequalities for embedded disks spanning unknotted curves. Zbl 1104.53006
Hass, Joel; Lagarias, Jeffrey C.; Thurston, William P.
2004
Approximate squaring. Zbl 1115.11045
Lagarias, J. C.; Sloane, N. J. A.
2004
Repetitive Delone sets and quasicrystals. Zbl 1062.52021
Lagarias, Jeffrey C.; Pleasants, Peter A. B.
2003
Apollonian circle packings: Number theory. Zbl 1026.11058
Graham, Ronald L.; Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R.; Yan, Catherine H.
2003
Substitution Delone sets. Zbl 1037.52017
Lagarias, Jeffrey C.; Wang, Yang
2003
On a two-variable zeta function for number fields. Zbl 1106.11036
Lagarias, Jeffrey C.; Rains, Eric
2003
Bounds for the $$3x+1$$ problem using difference inequalities. Zbl 1069.11011
Krasikov, Ilia; Lagarias, Jeffrey C.
2003
Lower bounds for the total stopping time of $$3x + 1$$ iterates. Zbl 1052.11017
Applegate, David; Lagarias, Jeffrey C.
2003
The minimal number of triangles needed to span a polygon embedded in $$\mathbb R^d$$. Zbl 1103.52013
Hass, Joel; Lagarias, Jeffrey C.
2003
Correction to: Linear fractional transformations of continued fractions with bounded partial quotients. Zbl 1071.11509
Lagarias, Jeffrey C.; Shallit, Jeffrey O.
2003
Beyond the Descartes circle theorem. Zbl 1027.51022
Lagarias, Jeffrey C.; Mallows, Colin L.; Wilks, Allan R.
2002
An elementary problem equivalent to the Riemann hypothesis. Zbl 1098.11005
Lagarias, Jeffrey C.
2002
Local complexity of Delone sets and crystallinity. Zbl 1016.52013
Lagarias, Jeffrey C.; Pleasants, Peter A. B.
2002
Pinwheel scheduling: Achievable densities. Zbl 1016.68007
Fishburn, P. C.; Lagarias, J. C.
2002
Counting dyadic equipartitions of the unit square. Zbl 1007.05013
Lagarias, Jeffrey C.; Spencer, Joel H.; Vinson, Jade P.
2002
Bounds for local density of sphere packings and the Kepler conjecture. Zbl 1005.52011
Lagarias, J. C.
2002
The number of Reidemeister moves needed for unknotting. Zbl 0964.57005
Hass, Joel; Lagarias, Jeffrey C.
2001
Corrigendum/addendum to: Sets of matrices all infinite products of which converge. Zbl 0978.15024
Daubechies, Ingrid; Lagarias, Jeffrey C.
2001
Universal spectra and Tijdeman’s conjecture on factorization of cyclic groups. Zbl 0988.47006
Lagarias, Jeffrey C.; Szabó, Sándor
2001
On the robustness of single-loop sigma-delta modulation. Zbl 1018.94520
Güntürk, C. Sinan; Lagarias, Jeffrey C.; Vaishampayan, Vinay A.
2001
Cutting sequences for geodesic flow on the modular surface and continued fractions. Zbl 1040.37008
Grabiner, David J.; Lagarias, Jeffrey C.
2001
On the normality of arithmetical constants. Zbl 1015.11036
Lagarias, Jeffrey C.
2001
Orthonormal bases of exponentials for the $$n$$-cube. Zbl 0978.42007
Lagarias, Jeffrey C.; Reeds, James A.; Wang, Yang
2000
Mathematical quasicrystals and the problem of diffraction. Zbl 1161.52312
Lagarias, Jeffrey C.
2000
Orthogonality criteria for compactly supported refinable functions and refinable function vectors. Zbl 0952.42017
Lagarias, Jeffrey C.; Wang, Yang
2000
Well-spaced labelings of points in rectangular grids. Zbl 0974.90022
Lagarias, Jeffrey C.
2000
The lap-counting and zeta functions of the tent map. Zbl 1003.37024
Flatto, Leopold; Lagarias, Jeffrey C.
2000
Complements to Li’s criterion for the Riemann Hypothesis. Zbl 0972.11079
Bombieri, Enrico; Lagarias, Jeffrey C.
1999
The computational complexity of knot and link problems. Zbl 1065.68667
Hass, Joel; Lagarias, Jeffrey C.; Pippenger, Nicholas
1999
Geometric models for quasicrystals. I. Delone sets of finite type. Zbl 0924.68190
Lagarias, J. C.
1999
Corrigendum/Addendum: Haar bases for $$L^2 (\mathbb{R}^n)$$ and algebraic number theory. Zbl 1007.11066
Lagarias, Jeffrey C.; Wang, Yang
1999
Geometric models for quasicrystals. II. Local rules under isometries. Zbl 0930.51019
Lagarias, J. C.
1999
On a positivity property of the Riemann $$\xi$$-function. Zbl 0928.11035
Lagarias, Jeffrey
1999
Number theory zeta functions and dynamical zeta functions. Zbl 0945.11018
Lagarias, Jeffrey C.
1999
Beurling generalized integers with the Delone property. Zbl 0927.11047
Lagarias, Jeffrey C.
1999
Convergence properties of the Nelder–Mead simplex method in low dimensions. Zbl 1005.90056
Lagarias, Jeffrey C.; Reeds, James A.; Wright, Margaret H.; Wright, Paul E.
1998
Multiregular point systems. Zbl 0915.51017
Dolbilin, N. P.; Lagarias, J. C.; Senechal, M.
1998
Threading homotopies and dc operating points of nonlinear circuits. Zbl 0994.65058
Geoghegan, Ross; Lagarias, Jeffrey C.; Melville, Robert C.
1998
Counting $$d$$-step paths in extremal Dantzig figures. Zbl 0899.52008
Lagarias, J. C.; Prabhu, N.
1998
Interference-minimizing colorings of regular graphs. Zbl 0912.05036
Fishburn, P. C.; Kim, J. H.; Lagarias, J. C.; Wright, P. E.
1998
Integral self-affine tiles in $$\mathbb{R}^n$$. II: Lattice tilings. Zbl 0893.52015
Lagarias, Jeffrey C.; Wang, Yang
1997
Spectral sets and factorizations of finite abelian groups. Zbl 0898.47002
Lagarias, Jeffrey C.; Wang, Yang
1997
Linear fractional transformations of continued fractions with bounded partial quotients. Zbl 0901.11024
Lagarias, J. C.; Shallit, J. O.
1997
The lap-counting function for linear mod one transformations. III: The period of a Markov chain. Zbl 0979.37018
Flatto, Leopold; Lagarias, Jeffrey C.
1997
Convexity and the average curvature of plane curves. Zbl 0887.53002
Lagarias, Jeffrey C.; Richardson, Thomas J.
1997
The lap-counting function for linear mod one transformations. II: The Markov chain for generalized lap numbers. Zbl 0979.37017
Flatto, Leopold; Lagarias, Jeffrey C.
1997
The $$3x+1$$ problem and its generalizations. (Reprint). Zbl 0883.11009
Lagarias, Jeffrey C.
1997
The $$d$$-step conjecture and Gaussian elimination. Zbl 0883.52008
Lagarias, J. C.; Prabhu, N.; Reeds, J. A.
1997
Self-affine tiles in $$\mathbb{R}^n$$. Zbl 0893.52013
Lagarias, Jeffrey C.; Wang, Yang
1996
...and 93 more Documents
all top 5

#### Cited by 3,236 Authors

 53 Lagarias, Jeffrey C. 22 Jørgensen, Palle E. T. 22 Shparlinski, Igor E. 21 Akiyama, Shigeki 20 Lau, Kasing 19 Wang, Yang 18 Protasov, Vladimir Yu. 17 Lenz, Daniel H. 17 Thuswaldner, Jörg Maximilian 15 Dubickas, Artūras 14 Dutkay, Dorin Ervin 14 Guglielmi, Nicola 13 He, Xinggang 13 Lai, Chun-Kit 12 Kozyakin, Viktor Sergeevich 12 Ngai, Sze-Man 12 Tsuchiya, Akiyoshi 12 Yang, Shouzhi 11 Gabardo, Jean-Pierre 11 Klein, Christian 11 Kolountzakis, Mihail N. 11 Ye, Yinyu 10 Ben Slimane, Mourad 10 Berthé, Valérie 10 Loridant, Benoit 10 Murty, Maruti Ram 10 Omar, Sami 10 Rémila, Eric 9 Charina, Maria 9 Lee, Jeong-Yup 9 Mazhouda, Kamel 9 Morris, Ian D. 9 Vallejo, Ernesto 9 Zhou, Dingxuan 9 Zhou, Xinlong 8 Dai, Xinrong 8 Dai, Xiongping 8 Li, Jianlin 8 Monteiro, Renato D. C. 8 Moree, Pieter 8 Nill, Benjamin 8 Odžak, Almasa 8 Pak, Igor 8 Pedersen, Steen 8 Rao, Hui 8 Smajlović, Lejla 8 Strungaru, Nicolae 8 Sun, Qiyu 8 Suzuki, Masatoshi 8 Verger-Gaugry, Jean-Louis 7 Allaart, Pieter C. 7 Bailey, David Harold 7 Berenhaut, Kenneth S. 7 Berg, Lothar 7 Blondel, Vincent D. 7 Coffey, Mark William 7 Julien, Antoine 7 Jungers, Raphaël M. 7 Luo, Jun Jason 7 Morawiec, Janusz 7 Richard, Christoph 7 Schnorr, Claus Peter 7 Swanepoel, Konrad J. 7 Tsuchiya, Takashi 7 Xiao, Mingqing 7 Zong, Chuanming 6 Alvarez-Vázquez, Lino Jose 6 An, Lixiang 6 Averkov, Gennadiy 6 Baake, Michael 6 Bach, Eric 6 Conti, Costanza 6 Deng, Qirong 6 Dubuc, Serge 6 Dulio, Paolo 6 Feng, De-Jun 6 Fuchs, Elena D. 6 Jia, Rong-Qing 6 Kari, Jarkko 6 Kisielewicz, Andrzej Piotr 6 Lev, Nir 6 Martinez, Aurea 6 Martini, Horst 6 Matei, Basarab 6 Odlyzko, Andrew M. 6 Ostafe, Alina 6 Solomyak, Boris 6 Steiner, Wolfgang 6 Vázquez-Méndez, Miguel Ernesto 6 Zaïmi, Toufik Mostepha 6 Zaman, Asif 6 Zennaro, Marino 6 Zhuravlev, Vladimir Georgievich 5 Abid, Moez Ben 5 Bourgain, Jean 5 Bugeaud, Yann 5 Burton, Benjamin A. 5 Cai, Jin-Yi 5 Chevallier, Nicolas 5 Deléglise, Marc ...and 3,136 more Authors
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#### Cited in 489 Serials

 97 Journal of Number Theory 82 Linear Algebra and its Applications 77 Theoretical Computer Science 67 Mathematics of Computation 50 Mathematical Programming. Series A. Series B 47 Transactions of the American Mathematical Society 45 Journal of Mathematical Analysis and Applications 45 Discrete & Computational Geometry 38 Proceedings of the American Mathematical Society 36 Journal de Théorie des Nombres de Bordeaux 35 Discrete Mathematics 35 The Journal of Fourier Analysis and Applications 34 Advances in Mathematics 33 Monatshefte für Mathematik 32 Experimental Mathematics 30 Applied Mathematics and Computation 30 Journal of Functional Analysis 30 Ergodic Theory and Dynamical Systems 27 Applied and Computational Harmonic Analysis 24 International Journal of Number Theory 21 Journal of Combinatorial Theory. Series A 19 Annales de l’Institut Fourier 18 Discrete Applied Mathematics 18 Journal of Computational and Applied Mathematics 18 Journal of Optimization Theory and Applications 17 European Journal of Combinatorics 16 Acta Arithmetica 16 Journal of Approximation Theory 15 Computers & Mathematics with Applications 15 European Journal of Operational Research 14 Mathematische Annalen 14 Indagationes Mathematicae. New Series 13 Communications in Mathematical Physics 13 Automatica 13 International Journal of Wavelets, Multiresolution and Information Processing 12 Information Processing Letters 12 Israel Journal of Mathematics 12 Inventiones Mathematicae 12 Bulletin of the American Mathematical Society. New Series 12 Computational Optimization and Applications 11 Journal of Difference Equations and Applications 10 Journal d’Analyse Mathématique 10 Journal of Computer and System Sciences 10 Mathematische Zeitschrift 10 Results in Mathematics 10 Physica D 10 Constructive Approximation 10 Computational Statistics and Data Analysis 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 10 Journal of Theoretical Biology 9 Journal of Mathematical Physics 9 Journal of Statistical Physics 9 Mathematical Proceedings of the Cambridge Philosophical Society 9 The Mathematical Intelligencer 9 Archiv der Mathematik 9 Compositio Mathematica 9 Advances in Applied Mathematics 9 Journal of Global Optimization 9 Journal of Mathematical Sciences (New York) 9 Fractals 9 Finite Fields and their Applications 9 The Ramanujan Journal 9 Abstract and Applied Analysis 8 Rocky Mountain Journal of Mathematics 8 Geometriae Dedicata 8 Systems & Control Letters 8 Combinatorica 8 Journal of Cryptology 8 Annals of Operations Research 8 St. Petersburg Mathematical Journal 8 Discrete and Continuous Dynamical Systems 8 Mathematical Problems in Engineering 8 Proceedings of the Steklov Institute of Mathematics 7 Duke Mathematical Journal 7 Functiones et Approximatio. Commentarii Mathematici 7 Mathematics and Computers in Simulation 7 Mathematika 7 Topology and its Applications 7 Applied Mathematical Modelling 7 Pattern Recognition 7 Advances in Computational Mathematics 7 Acta Mathematica Sinica. English Series 6 Journal of Mathematical Biology 6 Nonlinearity 6 Journal of Differential Equations 6 Manuscripta Mathematica 6 Proceedings of the Japan Academy. Series A 6 Operations Research Letters 6 Algorithmica 6 Information and Computation 6 Computers & Operations Research 6 Journal of the American Mathematical Society 6 SIAM Journal on Discrete Mathematics 6 Designs, Codes and Cryptography 6 Geometric and Functional Analysis. GAFA 6 Foundations of Computational Mathematics 6 Science China. Mathematics 6 Research in the Mathematical Sciences 5 American Mathematical Monthly 5 Computer Methods in Applied Mechanics and Engineering ...and 389 more Serials
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#### Cited in 63 Fields

 801 Number theory (11-XX) 343 Convex and discrete geometry (52-XX) 297 Computer science (68-XX) 287 Harmonic analysis on Euclidean spaces (42-XX) 281 Dynamical systems and ergodic theory (37-XX) 276 Operations research, mathematical programming (90-XX) 264 Numerical analysis (65-XX) 215 Combinatorics (05-XX) 205 Measure and integration (28-XX) 125 Linear and multilinear algebra; matrix theory (15-XX) 112 Information and communication theory, circuits (94-XX) 79 Statistics (62-XX) 76 Probability theory and stochastic processes (60-XX) 73 Group theory and generalizations (20-XX) 73 Real functions (26-XX) 69 Functional analysis (46-XX) 69 Systems theory; control (93-XX) 67 Algebraic geometry (14-XX) 65 Manifolds and cell complexes (57-XX) 61 Approximations and expansions (41-XX) 58 Difference and functional equations (39-XX) 57 Biology and other natural sciences (92-XX) 54 Operator theory (47-XX) 45 Partial differential equations (35-XX) 40 Ordinary differential equations (34-XX) 36 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 34 Statistical mechanics, structure of matter (82-XX) 31 Functions of a complex variable (30-XX) 30 Calculus of variations and optimal control; optimization (49-XX) 27 Mechanics of deformable solids (74-XX) 26 Geometry (51-XX) 26 Quantum theory (81-XX) 25 Field theory and polynomials (12-XX) 25 Special functions (33-XX) 25 Abstract harmonic analysis (43-XX) 21 Mathematical logic and foundations (03-XX) 21 Topological groups, Lie groups (22-XX) 21 General topology (54-XX) 20 Differential geometry (53-XX) 19 Commutative algebra (13-XX) 17 Sequences, series, summability (40-XX) 15 Fluid mechanics (76-XX) 13 Optics, electromagnetic theory (78-XX) 10 Integral equations (45-XX) 9 Integral transforms, operational calculus (44-XX) 8 Global analysis, analysis on manifolds (58-XX) 7 General and overarching topics; collections (00-XX) 6 Order, lattices, ordered algebraic structures (06-XX) 6 Geophysics (86-XX) 5 History and biography (01-XX) 5 Relativity and gravitational theory (83-XX) 4 $$K$$-theory (19-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Algebraic topology (55-XX) 4 Mechanics of particles and systems (70-XX) 4 Classical thermodynamics, heat transfer (80-XX) 2 Nonassociative rings and algebras (17-XX) 2 Category theory; homological algebra (18-XX) 2 Potential theory (31-XX) 2 Mathematics education (97-XX) 1 General algebraic systems (08-XX) 1 Associative rings and algebras (16-XX) 1 Astronomy and astrophysics (85-XX)

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