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Bach, Eric

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Author ID: bach.eric Recent zbMATH articles by "Bach, Eric"
Published as: Bach, E.; Bach, Eric
Documents Indexed: 64 Publications since 1985, including 2 Books

Publications by Year

Citations contained in zbMATH Open

46 Publications have been cited 553 times in 479 Documents Cited by Year
Algorithmic number theory, Vol. 1: Efficient algorithms. Zbl 0873.11070
Bach, Eric; Shallit, Jeffrey
137
1996
One-dimensional quantum walks. Zbl 1323.81021
Ambainis, Andris; Bach, Eric; Nayak, Ashwin; Vishwanath, Ashvin; Watrous, John
100
2001
Explicit bounds for primality testing and related problems. Zbl 0701.11075
Bach, Eric
56
1990
Explicit bounds for primes in residue classes. Zbl 0853.11077
Bach, Eric; Sorenson, Jonathan
35
1996
One-dimensional quantum walks with absorbing boundaries. Zbl 1107.81010
Bach, Eric; Coppersmith, Susan; Goldschen, Marcel Paz; Joynt, Robert; Watrous, John
20
2004
Factoring with cyclotomic polynomials. Zbl 0661.10008
Bach, Eric; Shallit, Jeffrey
20
1989
Improved approximations for Euler products. Zbl 0842.11046
Bach, Eric
15
1995
Factor refinement. Zbl 0784.11058
Bach, Eric; Driscoll, James; Shallit, Jeffrey
15
1993
Analytic methods in the analysis and design of number-theoretic algorithms. Zbl 0572.10001
Bach, Eric
13
1985
How to generate factored random numbers. Zbl 0642.10003
Bach, Eric
11
1988
Comments on search procedures for primitive roots. Zbl 0931.11058
Bach, Eric
10
1997
Sums of divisors, perfect numbers and factoring. Zbl 0606.10003
Bach, Eric; Miller, Gary; Shallit, Jeffrey
10
1986
Sieve algorithms for perfect power testing. Zbl 0771.11049
Bach, Eric; Sorenson, Jonathan
9
1993
DNA models and algorithms for NP-complete problems. Zbl 0921.68028
Bach, Eric; Condon, Anne; Glaser, Elton; Tanguay, Celena
7
1998
Realistic analysis of some randomized algorithms. Zbl 0724.11069
Bach, Eric
7
1991
Toward a theory of Pollard’s rho method. Zbl 0716.11065
Bach, Eric
7
1991
Factoring polynomials using fewer random bits. Zbl 0699.12027
Bach, Eric; Shoup, Victor
7
1990
Results and estimates on pseudopowers. Zbl 0853.11103
Bach, Eric; Lukes, Richard; Shallit, Jeffrey; Williams, H. C.
6
1996
Asymptotic semismoothness probabilities. Zbl 0853.11079
Bach, Eric; Peralta, René
6
1996
Statistical evidence for small generating sets. Zbl 0784.11059
Bach, Eric; Huelsbergen, Lorenz
6
1993
A note on square roots in finite fields. Zbl 0718.11066
Bach, Eric
6
1990
Computing prime harmonic sums. Zbl 1204.11184
Bach, Eric; Klyve, Dominic; Sorenson, Jonathan P.
5
2009
On the number of distinct functional graphs of affine-linear transformations over finite fields. Zbl 1302.37064
Bach, Eric; Bridy, Andrew
4
2013
Improved asymptotic formulas for counting correlation immune Boolean functions. Zbl 1209.05013
Bach, Eric
4
2009
Tight bounds on the competitive ratio on accommodating sequences for the seat reservation problem. Zbl 1154.90405
Bach, Eric; Boyar, Joan; Epstein, Leah; Favrholdt, Lene M.; Jiang, Tao; Larsen, Kim S.; Lin, Guo-Hui; Van Stee, Rob
4
2003
Factoring polynomials over special finite fields. Zbl 0985.11060
Bach, Eric; von zur Gathen, Joachim; Lenstra, Hendrik W. jun.
4
2001
The complexity of number-theoretic constants. Zbl 1053.11544
Bach, Eric
4
1997
Weil bounds for singular curves. Zbl 0877.11038
Bach, Eric
3
1996
Bounds for the expected duration of the monopolist game. Zbl 1185.91063
Bach, Eric
2
2007
On testing for zero polynomials by a set of points with bounded precision. Zbl 0991.68156
Cai, Jin-Yi; Bach, Eric
2
2001
Moments in the duration of play. Zbl 0897.60082
Bach, Eric
2
1997
Exact analysis of a priority queue algorithm for random variate generation. Zbl 0869.65005
Bach, Eric
2
1994
A parallel approach in computing correlation immunity up to six variables. Zbl 1401.94153
Etherington, Carole J.; Anderson, Matthew W.; Bach, Eric; Butler, Jon T.; Stănică, Pantelimon
1
2016
Approximately counting semismooth integers. Zbl 1360.68914
Bach, Eric; Sorenson, Jonathan P.
1
2013
Iterative root approximation in \(p\)-adic numerical analysis. Zbl 1184.65051
Bach, Eric
1
2009
Phase transition of multivariate polynomial systems. Zbl 1170.68017
Fusco, Giordano; Bach, Eric
1
2009
The hardness of computing an eigenform. Zbl 1195.11167
Bach, Eric; Charles, Denis
1
2008
Efficient verification of Tunnell’s criterion. Zbl 1183.11015
Bach, Eric; Ryan, Nathan C.
1
2007
Phase transition of multivariate polynomial systems. Zbl 1169.68396
Fusco, Giordano; Bach, Eric
1
2007
On testing for zero polynomials by a set of points with bounded precision. Zbl 1045.68166
Cai, Jin-Yi; Bach, Eric
1
2003
Random bisection and evolutionary walks. Zbl 1042.60074
Bach, Eric
1
2001
Note on taking square-roots modulo \(N\). Zbl 0945.94017
Bach, Eric; Huber, Klaus
1
1999
Sheaf cohomology is \(\#\)P-hard. Zbl 0940.68065
Bach, Eric
1
1999
Tensor products and computability. Zbl 0842.68043
Bach, Eric
1
1994
Explicit bounds for primes in residue classes. Zbl 0819.11034
Bach, Eric; Sorenson, Jonathan
1
1994
Factor refinement. Zbl 0800.68492
Bach, Eric; Driscoll, James; Shallit, Jeffrey
1
1990
A parallel approach in computing correlation immunity up to six variables. Zbl 1401.94153
Etherington, Carole J.; Anderson, Matthew W.; Bach, Eric; Butler, Jon T.; Stănică, Pantelimon
1
2016
On the number of distinct functional graphs of affine-linear transformations over finite fields. Zbl 1302.37064
Bach, Eric; Bridy, Andrew
4
2013
Approximately counting semismooth integers. Zbl 1360.68914
Bach, Eric; Sorenson, Jonathan P.
1
2013
Computing prime harmonic sums. Zbl 1204.11184
Bach, Eric; Klyve, Dominic; Sorenson, Jonathan P.
5
2009
Improved asymptotic formulas for counting correlation immune Boolean functions. Zbl 1209.05013
Bach, Eric
4
2009
Iterative root approximation in \(p\)-adic numerical analysis. Zbl 1184.65051
Bach, Eric
1
2009
Phase transition of multivariate polynomial systems. Zbl 1170.68017
Fusco, Giordano; Bach, Eric
1
2009
The hardness of computing an eigenform. Zbl 1195.11167
Bach, Eric; Charles, Denis
1
2008
Bounds for the expected duration of the monopolist game. Zbl 1185.91063
Bach, Eric
2
2007
Efficient verification of Tunnell’s criterion. Zbl 1183.11015
Bach, Eric; Ryan, Nathan C.
1
2007
Phase transition of multivariate polynomial systems. Zbl 1169.68396
Fusco, Giordano; Bach, Eric
1
2007
One-dimensional quantum walks with absorbing boundaries. Zbl 1107.81010
Bach, Eric; Coppersmith, Susan; Goldschen, Marcel Paz; Joynt, Robert; Watrous, John
20
2004
Tight bounds on the competitive ratio on accommodating sequences for the seat reservation problem. Zbl 1154.90405
Bach, Eric; Boyar, Joan; Epstein, Leah; Favrholdt, Lene M.; Jiang, Tao; Larsen, Kim S.; Lin, Guo-Hui; Van Stee, Rob
4
2003
On testing for zero polynomials by a set of points with bounded precision. Zbl 1045.68166
Cai, Jin-Yi; Bach, Eric
1
2003
One-dimensional quantum walks. Zbl 1323.81021
Ambainis, Andris; Bach, Eric; Nayak, Ashwin; Vishwanath, Ashvin; Watrous, John
100
2001
Factoring polynomials over special finite fields. Zbl 0985.11060
Bach, Eric; von zur Gathen, Joachim; Lenstra, Hendrik W. jun.
4
2001
On testing for zero polynomials by a set of points with bounded precision. Zbl 0991.68156
Cai, Jin-Yi; Bach, Eric
2
2001
Random bisection and evolutionary walks. Zbl 1042.60074
Bach, Eric
1
2001
Note on taking square-roots modulo \(N\). Zbl 0945.94017
Bach, Eric; Huber, Klaus
1
1999
Sheaf cohomology is \(\#\)P-hard. Zbl 0940.68065
Bach, Eric
1
1999
DNA models and algorithms for NP-complete problems. Zbl 0921.68028
Bach, Eric; Condon, Anne; Glaser, Elton; Tanguay, Celena
7
1998
Comments on search procedures for primitive roots. Zbl 0931.11058
Bach, Eric
10
1997
The complexity of number-theoretic constants. Zbl 1053.11544
Bach, Eric
4
1997
Moments in the duration of play. Zbl 0897.60082
Bach, Eric
2
1997
Algorithmic number theory, Vol. 1: Efficient algorithms. Zbl 0873.11070
Bach, Eric; Shallit, Jeffrey
137
1996
Explicit bounds for primes in residue classes. Zbl 0853.11077
Bach, Eric; Sorenson, Jonathan
35
1996
Results and estimates on pseudopowers. Zbl 0853.11103
Bach, Eric; Lukes, Richard; Shallit, Jeffrey; Williams, H. C.
6
1996
Asymptotic semismoothness probabilities. Zbl 0853.11079
Bach, Eric; Peralta, René
6
1996
Weil bounds for singular curves. Zbl 0877.11038
Bach, Eric
3
1996
Improved approximations for Euler products. Zbl 0842.11046
Bach, Eric
15
1995
Exact analysis of a priority queue algorithm for random variate generation. Zbl 0869.65005
Bach, Eric
2
1994
Tensor products and computability. Zbl 0842.68043
Bach, Eric
1
1994
Explicit bounds for primes in residue classes. Zbl 0819.11034
Bach, Eric; Sorenson, Jonathan
1
1994
Factor refinement. Zbl 0784.11058
Bach, Eric; Driscoll, James; Shallit, Jeffrey
15
1993
Sieve algorithms for perfect power testing. Zbl 0771.11049
Bach, Eric; Sorenson, Jonathan
9
1993
Statistical evidence for small generating sets. Zbl 0784.11059
Bach, Eric; Huelsbergen, Lorenz
6
1993
Realistic analysis of some randomized algorithms. Zbl 0724.11069
Bach, Eric
7
1991
Toward a theory of Pollard’s rho method. Zbl 0716.11065
Bach, Eric
7
1991
Explicit bounds for primality testing and related problems. Zbl 0701.11075
Bach, Eric
56
1990
Factoring polynomials using fewer random bits. Zbl 0699.12027
Bach, Eric; Shoup, Victor
7
1990
A note on square roots in finite fields. Zbl 0718.11066
Bach, Eric
6
1990
Factor refinement. Zbl 0800.68492
Bach, Eric; Driscoll, James; Shallit, Jeffrey
1
1990
Factoring with cyclotomic polynomials. Zbl 0661.10008
Bach, Eric; Shallit, Jeffrey
20
1989
How to generate factored random numbers. Zbl 0642.10003
Bach, Eric
11
1988
Sums of divisors, perfect numbers and factoring. Zbl 0606.10003
Bach, Eric; Miller, Gary; Shallit, Jeffrey
10
1986
Analytic methods in the analysis and design of number-theoretic algorithms. Zbl 0572.10001
Bach, Eric
13
1985
all top 5

Cited by 780 Authors

18 Bach, Eric
13 Konno, Norio
10 Segawa, Etsuo
9 Shparlinski, Igor E.
7 D’Ariano, Giacomo Mauro
7 Perinotti, Paolo
7 Sorenson, Jonathan P.
7 Williams, Hugh Cowie
6 Rojas, J. Maurice
6 Suzuki, Akito
6 von zur Gathen, Joachim
5 Buchmann, Johannes A.
5 Grünbaum, Francisco Alberto
5 Jacobson, Michael John jun.
5 Miret, Josep M.
5 Shallit, Jeffrey O.
5 Stein, Andreas
5 Sutherland, Andrew V.
5 Tosini, Alessandro
4 Belabas, Karim
4 Bisio, Alessandro
4 Cheng, Qi
4 Gao, Shuhong
4 Hancock, Edwin Robert
4 Karpinski, Marek
4 Lenstra, Hendrik W. jun.
4 Molteni, Giuseppe
4 Moree, Pieter
4 Peralta, René C.
4 Pollack, Paul
4 Rio, Anna
4 Sato, Iwao
4 Scheidler, Renate
4 Shoup, Victor
4 Treviño, Enrique
4 Velázquez, Luis
3 Berrizbeitia, Pedro
3 Boyar, Joan F.
3 Cai, Jin-Yi
3 Cheon, Jung Hee
3 Cohen, Henri
3 Emms, David M.
3 Frandsen, Gudmund Skovbjerg
3 Garton, Derek
3 Grenié, Loïc
3 Ivanyos, Gábor
3 Kendon, Viv M.
3 Klüners, Jürgen
3 Kuklinski, Parker
3 Li, Dan
3 Liu, Chaobin
3 Maurer, Ueli M.
3 McGown, Kevin J.
3 Moreno, Ramiro
3 Ohno, Hiromichi
3 Pujolàs, Jordi
3 Roblot, Xavier-François
3 Werner, Albert H.
3 Wilson, Richard Charles
3 Winterhof, Arne
3 Ying, Mingsheng
3 Yoo, Hyun Jae
3 Zrałek, Bartosz
2 Ahn, Jeoung-Hwan
2 Akchiche, Omar
2 Avendano, Martin
2 Baryshnikov, Yuliy M.
2 Bernstein, Daniel Julius
2 Biasse, Jean-François
2 Bisson, Gaetan
2 Blanchet-Sadri, Francine
2 Bridy, Andrew
2 Busch, Thomas
2 Cedzich, Christopher
2 Chandrashekar, C. M.
2 Cho, Ilwoo
2 Damgård, Ivan Bjerre
2 Deléglise, Marc
2 Diaz y Diaz, Francisco
2 Doerr, Benjamin
2 Eisenbrand, Friedrich
2 Favrholdt, Lene Monrad
2 Felix, Adam Tyler
2 Fernández Pérez, José Luis
2 Fidaleo, Francesco
2 Fouz, Mahmoud
2 Freivalds, Rūsiņš Mārtiņš
2 Friedman, Eduardo C.
2 Gashkov, Igor B.
2 Gashkov, Sergey B.
2 Geib, T.
2 Giesbrecht, Mark W.
2 Jørgensen, Palle E. T.
2 Kang, Yuanbao
2 Khadir, Omar
2 Kiltz, Eike
2 Kim, Henry H.
2 Knopfmacher, Arnold
2 Ko, Chul Ki
2 Kondratyonok, Nikita
...and 680 more Authors
all top 5

Cited in 148 Serials

73 Mathematics of Computation
33 Quantum Information Processing
22 Theoretical Computer Science
18 Journal of Symbolic Computation
17 Journal of Number Theory
16 Information Processing Letters
12 Finite Fields and their Applications
9 Journal of Computer and System Sciences
7 Discrete Applied Mathematics
7 Proceedings of the American Mathematical Society
7 Journal of Complexity
7 Designs, Codes and Cryptography
7 Journal de Théorie des Nombres de Bordeaux
6 Information and Computation
6 Journal of Cryptology
5 International Journal of Foundations of Computer Science
5 Applicable Algebra in Engineering, Communication and Computing
5 Computational Complexity
5 International Journal of Number Theory
5 Journal of Physics A: Mathematical and Theoretical
4 Communications in Mathematical Physics
4 Letters in Mathematical Physics
4 Linear Algebra and its Applications
4 Theory of Computing Systems
3 Computers & Mathematics with Applications
3 Discrete Mathematics
3 International Journal of Theoretical Physics
3 Journal of Mathematical Physics
3 Journal of Statistical Physics
3 Physica A
3 Acta Arithmetica
3 Journal of Algebra
3 Algorithmica
3 Pattern Recognition
3 Experimental Mathematics
3 Foundations of Physics
3 Quantum Studies: Mathematics and Foundations
2 Acta Informatica
2 Computer Physics Communications
2 Journal of Mathematical Analysis and Applications
2 Moscow University Mathematics Bulletin
2 Physics Letters. A
2 Reports on Mathematical Physics
2 Rocky Mountain Journal of Mathematics
2 Reviews in Mathematical Physics
2 The Mathematical Intelligencer
2 Annales de l’Institut Fourier
2 Functiones et Approximatio. Commentarii Mathematici
2 Journal of Computational and Applied Mathematics
2 Mathematische Annalen
2 Proceedings of the Japan Academy. Series A
2 SIAM Journal on Computing
2 Transactions of the American Mathematical Society
2 European Journal of Combinatorics
2 International Journal of Algebra and Computation
2 Infinite Dimensional Analysis, Quantum Probability and Related Topics
2 LMS Journal of Computation and Mathematics
2 Integers
2 Natural Computing
2 Algebra & Number Theory
2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 International Journal of Modern Physics B
1 American Mathematical Monthly
1 Archive for Rational Mechanics and Analysis
1 Bulletin of the Australian Mathematical Society
1 Periodica Mathematica Hungarica
1 Acta Mathematica Vietnamica
1 Advances in Mathematics
1 Annals of the Institute of Statistical Mathematics
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 Archiv der Mathematik
1 Automatica
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of Approximation Theory
1 Journal of Combinatorial Theory. Series B
1 Journal of the Mathematical Society of Japan
1 Journal of Soviet Mathematics
1 Mathematical Systems Theory
1 Pacific Journal of Mathematics
1 Quaestiones Mathematicae
1 Rendiconti del Circolo Matemàtico di Palermo. Serie II
1 Advances in Applied Mathematics
1 Statistics & Probability Letters
1 Physica D
1 Probability Theory and Related Fields
1 Mathematical and Computer Modelling
1 SIAM Journal on Discrete Mathematics
1 Formal Aspects of Computing
1 Sugaku Expositions
1 Neural Computation
1 Computational Geometry
1 MSCS. Mathematical Structures in Computer Science
1 Discrete Mathematics and Applications
1 Annals of Physics
1 European Journal of Operational Research
1 International Journal of Computer Mathematics
1 Bulletin of the American Mathematical Society. New Series
1 Mathematical Programming. Series A. Series B
1 Cybernetics and Systems Analysis
1 Combinatorics, Probability and Computing
...and 48 more Serials
all top 5

Cited in 38 Fields

249 Number theory (11-XX)
152 Computer science (68-XX)
87 Quantum theory (81-XX)
62 Probability theory and stochastic processes (60-XX)
53 Combinatorics (05-XX)
50 Information and communication theory, circuits (94-XX)
42 Statistical mechanics, structure of matter (82-XX)
32 Algebraic geometry (14-XX)
19 Field theory and polynomials (12-XX)
18 Numerical analysis (65-XX)
12 Dynamical systems and ergodic theory (37-XX)
12 Operations research, mathematical programming (90-XX)
10 Mathematical logic and foundations (03-XX)
10 Group theory and generalizations (20-XX)
9 Functional analysis (46-XX)
9 Operator theory (47-XX)
7 Commutative algebra (13-XX)
7 Partial differential equations (35-XX)
6 Linear and multilinear algebra; matrix theory (15-XX)
5 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
5 Biology and other natural sciences (92-XX)
3 Associative rings and algebras (16-XX)
3 Harmonic analysis on Euclidean spaces (42-XX)
2 Functions of a complex variable (30-XX)
2 Ordinary differential equations (34-XX)
2 Calculus of variations and optimal control; optimization (49-XX)
2 Differential geometry (53-XX)
2 Statistics (62-XX)
2 Relativity and gravitational theory (83-XX)
1 Special functions (33-XX)
1 Approximations and expansions (41-XX)
1 Geometry (51-XX)
1 Convex and discrete geometry (52-XX)
1 Manifolds and cell complexes (57-XX)
1 Global analysis, analysis on manifolds (58-XX)
1 Mechanics of particles and systems (70-XX)
1 Optics, electromagnetic theory (78-XX)
1 Mathematics education (97-XX)

Citations by Year