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## Morton, Patrick

Compute Distance To:
 Author ID: morton.patrick Published as: Morton, Patrick; Morton, P.
 Documents Indexed: 63 Publications since 1976
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#### Co-Authors

 32 single-authored 7 Minevich, Igor 5 Bremner, Andrew 5 Brillhart, John 3 Lewis, Donald-J. 2 Batra, Anjula 2 Calderbank, Arthur Robert 2 Mourant, W. J. 2 Silverman, Joseph Hillel 1 Allouche, Jean-Paul Simon 1 Boyd, David William 1 Cook, Janice 1 Erdős, Pál 1 Hanlon, Phil 1 Lomont, John S. 1 Lynch, Rodney 1 Patel, Pratiksha 1 Shallit, Jeffrey O. 1 Vivaldi, Franco 1 Wolfskill, John
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#### Serials

 9 Journal of Number Theory 6 Journal für die Reine und Angewandte Mathematik 3 American Mathematical Monthly 3 Acta Arithmetica 3 The New York Journal of Mathematics 3 The Ramanujan Journal 2 Rocky Mountain Journal of Mathematics 2 Compositio Mathematica 2 Journal of Geometry 2 Pacific Journal of Mathematics 2 Proceedings of the London Mathematical Society. Third Series 2 Journal of the Australian Mathematical Society. Series A 2 Forum Geometricorum 2 International Journal of Number Theory 2 International Journal of Geometry 1 Houston Journal of Mathematics 1 Nonlinearity 1 Mathematics of Computation 1 Archiv der Mathematik 1 Dissertationes Mathematicae 1 Functiones et Approximatio. Commentarii Mathematici 1 Illinois Journal of Mathematics 1 Journal of Algebra 1 Journal of the Faculty of Science. Section I A 1 Manuscripta Mathematica 1 The Quarterly Journal of Mathematics. Oxford Second Series 1 Studia Scientiarum Mathematicarum Hungarica 1 Theoretical Computer Science 1 SIAM Journal on Discrete Mathematics 1 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 1 IMRN. International Mathematics Research Notices 1 Finite Fields and their Applications 1 Journal for Geometry and Graphics
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#### Fields

 55 Number theory (11-XX) 16 Algebraic geometry (14-XX) 13 Field theory and polynomials (12-XX) 10 Dynamical systems and ergodic theory (37-XX) 7 Geometry (51-XX) 3 Combinatorics (05-XX) 3 Computer science (68-XX) 2 Real functions (26-XX) 2 Information and communication theory, circuits (94-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Special functions (33-XX)

#### Citations contained in zbMATH Open

51 Publications have been cited 434 times in 242 Documents Cited by Year
Rational periodic points of rational functions. Zbl 0819.11045
Morton, Patrick; Silverman, Joseph H.
1994
Periodic points, multiplicities, and dynamical units. Zbl 0813.11059
Morton, Patrick; Silverman, Joseph H.
1995
Arithmetic properties of periodic points of quadratic maps. II. Zbl 1029.12002
Morton, Patrick
1998
Class numbers of quadratic fields, Hasse invariants of elliptic curves, and the supersingular polynomial. Zbl 1083.11036
Brillhart, John; Morton, Patrick
2004
The Galois theory of periodic points of polynomial maps. Zbl 0792.11043
Morton, Patrick; Patel, Pratiksha
1994
On certain algebraic curves related to polynomial maps. Zbl 0860.11065
Morton, Patrick
1996
Arithmetic properties of periodic points of quadratic maps. Zbl 0767.11016
Morton, Patrick
1992
Bifurcations and discriminants for polynomial maps. Zbl 0827.12001
Morton, Patrick; Vivaldi, Franco
1995
Algebraic dynamics of polynomial maps on the algebraic closure of a finite field. I. Zbl 0810.11071
Batra, Anjula; Morton, Patrick
1994
Paper folding, digit patterns and groups of arithmetic fractals. Zbl 0694.10009
Morton, Patrick; Mourant, W. J.
1989
On sums of Rudin-Shapiro coefficients. II. Zbl 0469.10034
Brillhart, John; Erdős, Paul; Morton, Patrick
1983
Characterizing cyclic cubic extensions by automorphism polynomials. Zbl 0810.12003
Morton, Patrick
1994
Explicit identities for invariants of elliptic curves. Zbl 1193.11062
Morton, Patrick
2006
Quasi-symmetric 3-designs and elliptic curves. Zbl 0742.05013
Calderbank, A. R.; Morton, Patrick
1990
Über Summen von Rudin-Shapiroschen Koeffizienten. Zbl 0371.10009
Brillhart, John; Morton, Patrick
1978
On the eigenvectors of Schur’s matrix. Zbl 0428.10020
Morton, Patrick
1980
Density results for the 2-classgroups of imaginary quadratic fields. Zbl 0491.12004
Morton, Patrick
1982
The cubic Fermat equation and complex multiplication on the Deuring normal form. Zbl 1277.11029
Morton, Patrick
2011
Legendre polynomials and complex multiplication. I. Zbl 1200.11093
Morton, Patrick
2010
Some varieties with points only in a field extension. Zbl 0532.14011
Bremner, Andrew; Lewis, D. J.; Morton, Patrick
1984
Algebraic dynamics of polynomial maps on the algebraic closure of a finite field. II. Zbl 0816.11064
Batra, Anjula; Morton, Patrick
1994
Cyclotomic properties of the Rudin-Shapiro polynomials. Zbl 0335.12003
Brillhart, John; Lomont, J. S.; Morton, Patrick
1976
Two-weight ternary codes and the equation $$y^2=4 \times 3^\alpha+13$$. Zbl 0517.94012
Bremner, A.; Calderbank, R.; Hanlon, P.; Morton, P.; Wolfskill, J.
1983
Galois groups of periodic points. Zbl 0913.12005
Morton, Patrick
1998
A case study in mathematical research: The Golay-Rudin-Shapiro sequence. Zbl 0873.11020
Brillhart, John; Morton, Patrick
1996
On Redei’s theory of the Pell equation. Zbl 0395.12018
Morton, Patrick
1979
Digit patterns and transcendental numbers. Zbl 0746.11029
Morton, Patrick; Mourant, W. J.
1991
The integer points on three related elliptic curves. Zbl 0487.10014
Bremner, Andrew; Morton, Patrick
1982
Solutions of Diophantine equations as periodic points of $$p$$-adic algebraic functions. I. Zbl 1419.11059
Morton, Patrick
2016
Periods of maps on irreducible polynomials over finite fields. Zbl 0912.11051
Morton, Patrick
1997
Pattern spectra, substring enumeration, and automatic sequences. Zbl 0753.11012
Allouche, Jean-Paul; Morton, Patrick; Shallit, Jeffrey
1992
Connections between binary patterns and paperfolding. Zbl 0731.11016
Morton, Patrick
1990
The quadratic number fields with cyclic 2-classgroups. Zbl 0529.12004
Morton, Patrick
1983
On sequences of $$\pm 1's$$ defined by binary patterns. Zbl 0684.10011
Boyd, David W.; Cook, Janice; Morton, Patrick
1989
Synthetic foundations of Cevian geometry. III: The generalized orthocenter. Zbl 1377.51002
Minevich, Igor; Morton, Patrick
2017
Solutions of the cubic Fermat equation in ring class fields of imaginary quadratic fields (as periodic points of a 3-adic algebraic function). Zbl 1415.11063
Morton, Patrick
2016
Polynomial relations in characteristic p. Zbl 0391.12011
Bremner, Andrew; Morton, Patrick
1978
Explicit congruences for class equations. Zbl 1364.11112
Morton, Patrick
2014
Synthetic foundations of cevian geometry. II: The center of the cevian conic. Zbl 1372.51014
Minevich, Igor; Morton, Patrick
2016
The quartic Fermat equation in Hilbert class fields of imaginary quadratic fields. Zbl 1390.11064
Lynch, Rodney; Morton, Patrick
2015
Solutions of Diophantine equations as periodic points of $$p$$-adic algebraic functions. II: The Rogers-Ramanujan continued fraction. Zbl 1441.11064
Morton, Patrick
2019
A quadrilateral half-turn theorem. Zbl 1341.51021
Minevich, Igor; Morton, Patrick
2016
Synthetic foundations of cevian geometry. I: Fixed points of affine maps. Zbl 1370.51019
Minevich, Igor; Morton, Patrick
2017
Product formulas for the 5-division points on the Tate normal form and the Rogers-Ramanujan continued fraction. Zbl 1443.11098
Morton, Patrick
2019
A new characterization of the integer 5906. Zbl 0516.10012
Bremner, Andrew; Morton, Patrick
1983
Corrigendum: “On certain algebraic curves related to polynomial maps”. Zbl 1264.11091
Morton, Patrick
2011
Density results for the 2-classgroups and fundamental units of real quadratic fields. Zbl 0548.12001
Morton, Patrick
1982
Vertex positions of the generalized orthocenter and a related elliptic curve. Zbl 1383.51002
Minevich, Igor; Morton, Patrick
2017
A generalization of Zolotarev’s theorem. Zbl 0418.10003
Morton, Patrick
1979
Periodic points of algebraic functions and Deuring’s class number formula. Zbl 1461.14033
Morton, Patrick
2019
On the Hasse invariants of the Tate normal forms $$E_5$$ and $$E_7$$. Zbl 07257228
Morton, Patrick
2021
On the Hasse invariants of the Tate normal forms $$E_5$$ and $$E_7$$. Zbl 07257228
Morton, Patrick
2021
Solutions of Diophantine equations as periodic points of $$p$$-adic algebraic functions. II: The Rogers-Ramanujan continued fraction. Zbl 1441.11064
Morton, Patrick
2019
Product formulas for the 5-division points on the Tate normal form and the Rogers-Ramanujan continued fraction. Zbl 1443.11098
Morton, Patrick
2019
Periodic points of algebraic functions and Deuring’s class number formula. Zbl 1461.14033
Morton, Patrick
2019
Synthetic foundations of Cevian geometry. III: The generalized orthocenter. Zbl 1377.51002
Minevich, Igor; Morton, Patrick
2017
Synthetic foundations of cevian geometry. I: Fixed points of affine maps. Zbl 1370.51019
Minevich, Igor; Morton, Patrick
2017
Vertex positions of the generalized orthocenter and a related elliptic curve. Zbl 1383.51002
Minevich, Igor; Morton, Patrick
2017
Solutions of Diophantine equations as periodic points of $$p$$-adic algebraic functions. I. Zbl 1419.11059
Morton, Patrick
2016
Solutions of the cubic Fermat equation in ring class fields of imaginary quadratic fields (as periodic points of a 3-adic algebraic function). Zbl 1415.11063
Morton, Patrick
2016
Synthetic foundations of cevian geometry. II: The center of the cevian conic. Zbl 1372.51014
Minevich, Igor; Morton, Patrick
2016
A quadrilateral half-turn theorem. Zbl 1341.51021
Minevich, Igor; Morton, Patrick
2016
The quartic Fermat equation in Hilbert class fields of imaginary quadratic fields. Zbl 1390.11064
Lynch, Rodney; Morton, Patrick
2015
Explicit congruences for class equations. Zbl 1364.11112
Morton, Patrick
2014
The cubic Fermat equation and complex multiplication on the Deuring normal form. Zbl 1277.11029
Morton, Patrick
2011
Corrigendum: “On certain algebraic curves related to polynomial maps”. Zbl 1264.11091
Morton, Patrick
2011
Legendre polynomials and complex multiplication. I. Zbl 1200.11093
Morton, Patrick
2010
Explicit identities for invariants of elliptic curves. Zbl 1193.11062
Morton, Patrick
2006
Class numbers of quadratic fields, Hasse invariants of elliptic curves, and the supersingular polynomial. Zbl 1083.11036
Brillhart, John; Morton, Patrick
2004
Arithmetic properties of periodic points of quadratic maps. II. Zbl 1029.12002
Morton, Patrick
1998
Galois groups of periodic points. Zbl 0913.12005
Morton, Patrick
1998
Periods of maps on irreducible polynomials over finite fields. Zbl 0912.11051
Morton, Patrick
1997
On certain algebraic curves related to polynomial maps. Zbl 0860.11065
Morton, Patrick
1996
A case study in mathematical research: The Golay-Rudin-Shapiro sequence. Zbl 0873.11020
Brillhart, John; Morton, Patrick
1996
Periodic points, multiplicities, and dynamical units. Zbl 0813.11059
Morton, Patrick; Silverman, Joseph H.
1995
Bifurcations and discriminants for polynomial maps. Zbl 0827.12001
Morton, Patrick; Vivaldi, Franco
1995
Rational periodic points of rational functions. Zbl 0819.11045
Morton, Patrick; Silverman, Joseph H.
1994
The Galois theory of periodic points of polynomial maps. Zbl 0792.11043
Morton, Patrick; Patel, Pratiksha
1994
Algebraic dynamics of polynomial maps on the algebraic closure of a finite field. I. Zbl 0810.11071
Batra, Anjula; Morton, Patrick
1994
Characterizing cyclic cubic extensions by automorphism polynomials. Zbl 0810.12003
Morton, Patrick
1994
Algebraic dynamics of polynomial maps on the algebraic closure of a finite field. II. Zbl 0816.11064
Batra, Anjula; Morton, Patrick
1994
Arithmetic properties of periodic points of quadratic maps. Zbl 0767.11016
Morton, Patrick
1992
Pattern spectra, substring enumeration, and automatic sequences. Zbl 0753.11012
Allouche, Jean-Paul; Morton, Patrick; Shallit, Jeffrey
1992
Digit patterns and transcendental numbers. Zbl 0746.11029
Morton, Patrick; Mourant, W. J.
1991
Quasi-symmetric 3-designs and elliptic curves. Zbl 0742.05013
Calderbank, A. R.; Morton, Patrick
1990
Connections between binary patterns and paperfolding. Zbl 0731.11016
Morton, Patrick
1990
Paper folding, digit patterns and groups of arithmetic fractals. Zbl 0694.10009
Morton, Patrick; Mourant, W. J.
1989
On sequences of $$\pm 1's$$ defined by binary patterns. Zbl 0684.10011
Boyd, David W.; Cook, Janice; Morton, Patrick
1989
Some varieties with points only in a field extension. Zbl 0532.14011
Bremner, Andrew; Lewis, D. J.; Morton, Patrick
1984
On sums of Rudin-Shapiro coefficients. II. Zbl 0469.10034
Brillhart, John; Erdős, Paul; Morton, Patrick
1983
Two-weight ternary codes and the equation $$y^2=4 \times 3^\alpha+13$$. Zbl 0517.94012
Bremner, A.; Calderbank, R.; Hanlon, P.; Morton, P.; Wolfskill, J.
1983
The quadratic number fields with cyclic 2-classgroups. Zbl 0529.12004
Morton, Patrick
1983
A new characterization of the integer 5906. Zbl 0516.10012
Bremner, Andrew; Morton, Patrick
1983
Density results for the 2-classgroups of imaginary quadratic fields. Zbl 0491.12004
Morton, Patrick
1982
The integer points on three related elliptic curves. Zbl 0487.10014
Bremner, Andrew; Morton, Patrick
1982
Density results for the 2-classgroups and fundamental units of real quadratic fields. Zbl 0548.12001
Morton, Patrick
1982
On the eigenvectors of Schur’s matrix. Zbl 0428.10020
Morton, Patrick
1980
On Redei’s theory of the Pell equation. Zbl 0395.12018
Morton, Patrick
1979
A generalization of Zolotarev’s theorem. Zbl 0418.10003
Morton, Patrick
1979
Über Summen von Rudin-Shapiroschen Koeffizienten. Zbl 0371.10009
Brillhart, John; Morton, Patrick
1978
Polynomial relations in characteristic p. Zbl 0391.12011
Bremner, Andrew; Morton, Patrick
1978
Cyclotomic properties of the Rudin-Shapiro polynomials. Zbl 0335.12003
Brillhart, John; Lomont, J. S.; Morton, Patrick
1976
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#### Cited by 258 Authors

 24 Morton, Patrick 10 Doyle, John R. 8 Benedetto, Robert L. 8 Canci, Jung Kyu 7 Allouche, Jean-Paul Simon 7 Silverman, Joseph Hillel 7 Tucker, Thomas John 5 Bremner, Andrew 5 Bridy, Andrew 5 Cullinan, John 5 Hutz, Benjamin 5 Shallit, Jeffrey O. 4 Erdélyi, Tamás 4 Gerth, Frank III 4 Ghioca, Dragos 4 Hoshi, Akinari 4 Hsia, Liang-Chung 4 Ingram, Patrick 4 Krumm, David 4 Narkiewicz, Władysław 4 Vishkautsan, Solomon 4 Vivaldi, Franco 3 Hajir, Farshid 3 Manes, Michelle 3 Minevich, Igor 3 Raposa, Blessilda P. 3 Sane, Sharad S. 3 Tzanakis, Nikos 3 Wolfskill, John 2 Arias-de-Reyna, Sara 2 Batra, Anjula 2 Dumont, Jean-Marie 2 Flynn, Eugene Victor 2 Grabner, Peter J. 2 Kamae, Teturo 2 Komatsu, Toru 2 Kosunen, Pekka 2 Kurlberg, Pär 2 Lecouturier, Emmanuel 2 Mans, Bernard 2 Mukhamedov, Farruh Maksutovich 2 Nguyen Ngoc Dong Quan 2 Novoselov, S. A. 2 Pawale, Rajendra M. 2 Peng, Li 2 Poonen, Bjorn 2 Praeger, Cheryl Elisabeth 2 Rivera-Letelier, Juan 2 Roberts, John Anthony Gerard 2 Sell, Elizabeth A. 2 Sha, Min 2 Shparlinski, Igor E. 2 Shrikhande, Mohan S. 2 Thomas, Alain 2 Tichy, Robert Franz 2 Troncoso, Sebastian 2 Wen, Zhixiong 2 Zheng, Yu 1 Abdollahi, Abdolaziz 1 Adamczewski, Boris 1 Akbary, Amir 1 Akin, Hasan 1 Alzer, Horst 1 Amano, Fumiya 1 Anashin, Vladimir Sergeevich 1 Arias-de-Reyna, Juan 1 Baartmans, Alphonse H. 1 Bachoc, Christine 1 Bajguz, Wiesław 1 Beals, Robert M. 1 Benjamin, Elliot 1 Bennett, Michael A. 1 Berndt, Bruce Carl 1 Betina, Adel 1 Bézivin, Jean-Paul 1 Bogomolov, Fedor Alekseivich 1 Bondarenko, Andriy V. 1 Bosma, Wieb 1 Briend, Jean-Yves 1 Bruin, Nils 1 Brunyate, Adrian 1 Calderbank, Arthur Robert 1 Call, Gregory S. 1 Cassels, J. W. S. 1 Chen, Jin 1 Chen, Ruqian 1 Chen, Yi-Chiuan 1 Cheshmavar, Jahangir 1 Ciungu, Lavinia Corina 1 Clark, Peter Louis 1 Cohen, Stephen D. 1 Coons, Michael 1 Cusick, Thomas W. 1 Dahmen, Sander R. 1 de Faria, João Alberto 1 Divišová, Zuzana 1 Dow, R. A. 1 Dumas, Philippe 1 Eliahou, Shalom 1 Etropolski, Anastassia ...and 158 more Authors
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#### Cited in 99 Serials

 38 Journal of Number Theory 8 Proceedings of the American Mathematical Society 8 Theoretical Computer Science 8 International Journal of Number Theory 6 Compositio Mathematica 6 Transactions of the American Mathematical Society 6 The Ramanujan Journal 5 Journal de Théorie des Nombres de Bordeaux 4 Discrete Mathematics 4 Rocky Mountain Journal of Mathematics 4 Annales de l’Institut Fourier 4 Functiones et Approximatio. Commentarii Mathematici 4 Finite Fields and their Applications 3 Mathematics of Computation 3 Duke Mathematical Journal 3 Inventiones Mathematicae 3 Journal of Algebra 3 Journal of Combinatorial Theory. Series B 3 Manuscripta Mathematica 3 Mathematische Annalen 3 Mathematica Slovaca 3 Mathematische Zeitschrift 3 Monatshefte für Mathematik 3 Bulletin of the American Mathematical Society. New Series 3 Experimental Mathematics 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Mathematical Analysis and Applications 2 Acta Arithmetica 2 Advances in Mathematics 2 Illinois Journal of Mathematics 2 Journal of Approximation Theory 2 Journal of Combinatorial Theory. Series A 2 Journal of Geometry 2 Proceedings of the Japan Academy. Series A 2 Tokyo Journal of Mathematics 2 Advances in Applied Mathematics 2 Ergodic Theory and Dynamical Systems 2 Physica D 2 Designs, Codes and Cryptography 2 Linear Algebra and its Applications 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Indagationes Mathematicae. New Series 2 Conformal Geometry and Dynamics 2 Central European Journal of Mathematics 2 Proceedings of the Steklov Institute of Mathematics 2 Algebra & Number Theory 2 Science China. Mathematics 1 Discrete Applied Mathematics 1 Israel Journal of Mathematics 1 Journal d’Analyse Mathématique 1 Linear and Multilinear Algebra 1 Mathematical Notes 1 Nonlinearity 1 The Mathematical Intelligencer 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Archiv der Mathematik 1 Glasgow Mathematical Journal 1 Journal of Differential Equations 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Mathematika 1 Michigan Mathematical Journal 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Semigroup Forum 1 Bulletin of the Korean Mathematical Society 1 Acta Mathematica Hungarica 1 Graphs and Combinatorics 1 Journal of Symbolic Computation 1 Constructive Approximation 1 SIAM Journal on Matrix Analysis and Applications 1 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 1 IMRN. International Mathematics Research Notices 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Applied and Computational Harmonic Analysis 1 Annales Mathématiques Blaise Pascal 1 Acta Universitatis Matthiae Belii. Series Mathematics 1 Fractals 1 Advances in Applied Clifford Algebras 1 The New York Journal of Mathematics 1 Discrete and Continuous Dynamical Systems 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 Journal for Geometry and Graphics 1 Chaos 1 Annals of Mathematics. Second Series 1 LMS Journal of Computation and Mathematics 1 Integers 1 Physical Review Letters 1 Journal of Algebra and its Applications 1 International Journal of Quantum Information 1 Oberwolfach Reports 1 São Paulo Journal of Mathematical Sciences 1 Cryptography and Communications 1 RAIRO. Theoretical Informatics and Applications 1 Journal of Complex Analysis 1 Research in the Mathematical Sciences 1 Arnold Mathematical Journal 1 Research in Number Theory 1 Prikladnaya Diskretnaya Matematika
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#### Cited in 30 Fields

 168 Number theory (11-XX) 88 Dynamical systems and ergodic theory (37-XX) 58 Algebraic geometry (14-XX) 20 Combinatorics (05-XX) 17 Field theory and polynomials (12-XX) 15 Computer science (68-XX) 8 Functions of a complex variable (30-XX) 6 Special functions (33-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Information and communication theory, circuits (94-XX) 5 Commutative algebra (13-XX) 5 Group theory and generalizations (20-XX) 5 Geometry (51-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Several complex variables and analytic spaces (32-XX) 3 Measure and integration (28-XX) 3 Approximations and expansions (41-XX) 3 Numerical analysis (65-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Difference and functional equations (39-XX) 2 Probability theory and stochastic processes (60-XX) 2 Quantum theory (81-XX) 1 Associative rings and algebras (16-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Integral transforms, operational calculus (44-XX) 1 Operator theory (47-XX) 1 Convex and discrete geometry (52-XX) 1 Statistical mechanics, structure of matter (82-XX)