# zbMATH — the first resource for mathematics

Compute Distance To:
 Documents Indexed: 52 Publications since 1976, including 2 Books
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#### Co-Authors

 12 single-authored 38 Sperber, Steven I. 2 Dwork, Bernard Morris 1 Baldassarri, Francesco 1 Berthelot, Pierre 1 Katz, Nicholas Michael 1 Loeser, François 1 Tretkoff, Marvin D.
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#### Serials

 6 Transactions of the American Mathematical Society 4 American Journal of Mathematics 3 Duke Mathematical Journal 3 Algebra & Number Theory 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Compositio Mathematica 2 Illinois Journal of Mathematics 2 Inventiones Mathematicae 2 Journal of Algebra 2 Journal für die Reine und Angewandte Mathematik 2 Proceedings of the American Mathematical Society 2 Rendiconti del Seminario Matematico della Università di Padova 2 Finite Fields and their Applications 1 Israel Journal of Mathematics 1 Journal of Number Theory 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Nagoya Mathematical Journal 1 Pacific Journal of Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Annals of Mathematics. Second Series 1 Integers 1 International Journal of Number Theory 1 Contemporary Mathematics
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#### Fields

 40 Number theory (11-XX) 38 Algebraic geometry (14-XX) 9 Special functions (33-XX) 6 Field theory and polynomials (12-XX) 3 Commutative algebra (13-XX) 3 Convex and discrete geometry (52-XX) 2 General and overarching topics; collections (00-XX) 1 $$K$$-theory (19-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX)

#### Citations contained in zbMATH Open

43 Publications have been cited 327 times in 206 Documents Cited by Year
Hypergeometric functions and rings generated by monomials. Zbl 0804.33013
1994
Exponential sums and Newton polyhedra: cohomology and estimates. Zbl 0723.14017
1989
$$p$$-adic estimates for exponential sums and the theorem of Chevalley-Warning. Zbl 0654.12011
1987
Newton polyhedra and the degree of the L-function associated to an exponential sum. Zbl 0623.12012
1987
On the degree of the $$L$$-function associated with an exponential sum. Zbl 0665.12022
1988
Twisted exponential sums and Newton polyhedra. Zbl 0853.11067
1993
On the distribution of angles of Kloosterman sums. Zbl 0682.40002
1989
An index theorem for p-adic differential operators. Zbl 0297.47039
1976
On twisted exponential sums. Zbl 0716.11039
1991
Higher solutions of hypergeometric systems and Dwork cohomology. Zbl 0931.14012
1999
p-adic estimates for exponential sums. Zbl 0727.11056
1990
Exponential sums on the complement of a hypersurface. Zbl 0444.12016
1980
Distinguished-root formulas for generalized Calabi-Yau hypersurfaces. Zbl 1394.11054
2017
Hasse invariants and mod $$p$$ solutions of $$A$$-hypergeometric systems. Zbl 1295.11134
2014
On twisted de Rham cohomology. Zbl 0915.14012
1997
Exponential sums on $$(\mathbb{G}_ m)^ n$$. Zbl 0764.11037
1990
Twisted Kloosterman sums and $$p$$-adic Bessel functions. Zbl 0552.12010
1984
The $$U_p$$-operator of Atkin on modular functions of level three. Zbl 0431.14006
1980
A p-adic theory of Hecke polynomials. Zbl 0339.14012
1976
On unit root formulas for toric exponential sums. Zbl 1251.11081
2012
On the zeta function of a complete intersection. Zbl 0911.11030
1996
Exponential sums and Newton polyhedra. Zbl 0634.12018
1987
On the Dwork trace formula. Zbl 0552.12011
1984
$$A$$-hypergeometric series and the Hasse-Witt matrix of a hypersurface. Zbl 1416.11101
2016
$$A$$-hypergeometric systems that come from geometry. Zbl 1257.14016
2012
Exponential sums nondegenerate relative to a lattice. Zbl 1207.11082
2009
On the Jacobian ring of a complete intersection. Zbl 1110.14046
2006
Exponential sums on $$\mathbb{A}^n$$. Zbl 1034.11043
2000
Exponential sums on $$\mathbb{A}^n$$. III. Zbl 0987.11076
2000
Twisted Kloosterman sums and $$p$$-adic Bessel functions. II: Newton polygons and analytic continuation. Zbl 0633.12007
1987
Character sums in finite fields. Zbl 0561.12008
1984
On the zeta function of a projective complete intersection. Zbl 1232.11092
2008
Exponential sums on $$\mathbf{A}^n$$. II. Zbl 1125.11337
2004
Dwork cohomology, de Rham cohomology, and hypergeometric functions. Zbl 0980.14017
2000
Exponential sums on $$(\mathbb{F}_ q^*)^ n$$. Zbl 0764.11036
1990
Growth of solutions of linear differential equations at a logarithmic singularity. Zbl 0502.12017
Adolphson, A.; Dwork, B.; Sperber, S.
1982
On the integrality of factorial ratios and mirror maps. Zbl 1432.11068
2020
Exponential sums and generalized hypergeometric functions. I: Cohomology spaces and Frobenius action. Zbl 1100.11024
2004
Geometric aspects of Dwork theory. Vol. I, II. Zbl 1047.14001
Adolphson, Alan (ed.); Baldassarri, Francesco (ed.); Berthelot, Pierre (ed.); Katz, Nicholas (ed.); Loeser, François (ed.)
2004
On the degree of the zeta function of a complete intersection. Zbl 0946.14010
1999
Contiguity relations for generalized hypergeometric functions. Zbl 0814.33004
1995
Uniqueness of $$\Gamma _ p:$$ The locally analytic case. Zbl 0552.12009
1984
On the mod p eigenvalues of Hecke operators. Zbl 0339.14011
1976
On the integrality of factorial ratios and mirror maps. Zbl 1432.11068
2020
Distinguished-root formulas for generalized Calabi-Yau hypersurfaces. Zbl 1394.11054
2017
$$A$$-hypergeometric series and the Hasse-Witt matrix of a hypersurface. Zbl 1416.11101
2016
Hasse invariants and mod $$p$$ solutions of $$A$$-hypergeometric systems. Zbl 1295.11134
2014
On unit root formulas for toric exponential sums. Zbl 1251.11081
2012
$$A$$-hypergeometric systems that come from geometry. Zbl 1257.14016
2012
Exponential sums nondegenerate relative to a lattice. Zbl 1207.11082
2009
On the zeta function of a projective complete intersection. Zbl 1232.11092
2008
On the Jacobian ring of a complete intersection. Zbl 1110.14046
2006
Exponential sums on $$\mathbf{A}^n$$. II. Zbl 1125.11337
2004
Exponential sums and generalized hypergeometric functions. I: Cohomology spaces and Frobenius action. Zbl 1100.11024
2004
Geometric aspects of Dwork theory. Vol. I, II. Zbl 1047.14001
Adolphson, Alan (ed.); Baldassarri, Francesco (ed.); Berthelot, Pierre (ed.); Katz, Nicholas (ed.); Loeser, François (ed.)
2004
Exponential sums on $$\mathbb{A}^n$$. Zbl 1034.11043
2000
Exponential sums on $$\mathbb{A}^n$$. III. Zbl 0987.11076
2000
Dwork cohomology, de Rham cohomology, and hypergeometric functions. Zbl 0980.14017
2000
Higher solutions of hypergeometric systems and Dwork cohomology. Zbl 0931.14012
1999
On the degree of the zeta function of a complete intersection. Zbl 0946.14010
1999
On twisted de Rham cohomology. Zbl 0915.14012
1997
On the zeta function of a complete intersection. Zbl 0911.11030
1996
Contiguity relations for generalized hypergeometric functions. Zbl 0814.33004
1995
Hypergeometric functions and rings generated by monomials. Zbl 0804.33013
1994
Twisted exponential sums and Newton polyhedra. Zbl 0853.11067
1993
On twisted exponential sums. Zbl 0716.11039
1991
p-adic estimates for exponential sums. Zbl 0727.11056
1990
Exponential sums on $$(\mathbb{G}_ m)^ n$$. Zbl 0764.11037
1990
Exponential sums on $$(\mathbb{F}_ q^*)^ n$$. Zbl 0764.11036
1990
Exponential sums and Newton polyhedra: cohomology and estimates. Zbl 0723.14017
1989
On the distribution of angles of Kloosterman sums. Zbl 0682.40002
1989
On the degree of the $$L$$-function associated with an exponential sum. Zbl 0665.12022
1988
$$p$$-adic estimates for exponential sums and the theorem of Chevalley-Warning. Zbl 0654.12011
1987
Newton polyhedra and the degree of the L-function associated to an exponential sum. Zbl 0623.12012
1987
Exponential sums and Newton polyhedra. Zbl 0634.12018
1987
Twisted Kloosterman sums and $$p$$-adic Bessel functions. II: Newton polygons and analytic continuation. Zbl 0633.12007
1987
Twisted Kloosterman sums and $$p$$-adic Bessel functions. Zbl 0552.12010
1984
On the Dwork trace formula. Zbl 0552.12011
1984
Character sums in finite fields. Zbl 0561.12008
1984
Uniqueness of $$\Gamma _ p:$$ The locally analytic case. Zbl 0552.12009
1984
Growth of solutions of linear differential equations at a logarithmic singularity. Zbl 0502.12017
Adolphson, A.; Dwork, B.; Sperber, S.
1982
Exponential sums on the complement of a hypersurface. Zbl 0444.12016
1980
The $$U_p$$-operator of Atkin on modular functions of level three. Zbl 0431.14006
1980
An index theorem for p-adic differential operators. Zbl 0297.47039
1976
A p-adic theory of Hecke polynomials. Zbl 0339.14012
1976
On the mod p eigenvalues of Hecke operators. Zbl 0339.14011
1976
all top 5

#### Cited by 190 Authors

 27 Sperber, Steven I. 24 Adolphson, Alan 11 Matusevich, Laura Felicia 9 Castro, Francis Noel 8 Liu, Chunlei 8 Walther, Uli 7 Cao, Wei 7 Fernández-Fernández, María-Cruz 5 Castro-Jiménez, Francisco Jesús 5 Haessig, C. Douglas 5 Niu, ChuanZe 5 Takeuchi, Kiyoshi 4 Berkesch Zamaere, Christine 4 Dickenstein, Alicia M. 4 Hong, Shaofang 4 Lauder, Alan G. B. 4 Medina, Luis A. 4 Schulze, Mathias 4 Sevenheck, Christian 4 Takayama, Nobuki 3 Basu, Saugata 3 Beukers, Frits 3 Blache, Régis 3 Glazunov, Mykola Mykhaĭlovych 3 Iritani, Hiroshi 3 Liu, WenXin 3 Miller, Ezra 3 Ouyang, Yi 3 Reichelt, Thomas 3 Rubio, Ivelisse M. 3 Wan, Daqing 3 Zhu, Hui June 2 Bandman, Tatiana M. 2 Borisov, Lev A. 2 Coleman, Robert Frederick 2 Crew, Richard M. 2 Denef, Jan 2 Esterov, Alexander I. 2 Forsgård, Jens 2 Fu, Lei 2 González, Oscar E. 2 Hartillo-Hermoso, María Isabel 2 Horja, R. Paul 2 Katz, Nicholas Michael 2 Kunyavskiĭ, Boris Èmmanuilovich 2 Lachaud, Gilles 2 Matsubara-Heo, Saiei-Jaeyeong 2 Robba, Philippe 2 Rojas-León, Antonio 2 Saito, Mutsumi 2 Shparlinski, Igor E. 2 Smith, Luke B. 2 van der Put, Marius 2 Whitcher, Ursula A. 2 Yang, Jinbang 2 Yu, Jeng-Daw 2 Zúñiga-Galindo, Wilson A. 1 Achter, Jeffrey D. 1 Aggarwal, Keshav 1 Ando, Kana 1 André, Yves 1 Arcadias, Rémi 1 Artamonov, Dmitry V. 1 Balasubramanian, Ramachandran 1 Baldassarri, Francesco 1 Barone, Sal 1 Berthelot, Pierre 1 Castaño Domínguez, Alberto 1 Castro-Velez, F. N. 1 Castryck, Wouter 1 Cattani, Eduardo H. 1 Chapman, Robin J. 1 Chen, Chao 1 Chen, Hua 1 Chen, Jianming 1 Christol, Gilles 1 Cluckers, Raf 1 D’Andrea, Carlos 1 Dartyge, Cécile 1 Djanković, Goran 1 Dollarhide, John 1 Donovan, Will 1 Doran, Charles F. 1 Dwork, Bernard Morris 1 Esnault, Hélène 1 Fang, JiangXue 1 Feng, Weiduan 1 Férard, Éric 1 Figueroa, Raúl F. 1 Fischler, Stéphane 1 Fleming, Patrick S. 1 Fouvry, Etienne 1 Franc, Cameron 1 Fu, Lei 1 Gannon, Terry 1 García López, Ricardo 1 Garcia, Stephan Ramon 1 Garion, Shelly 1 Garnier, Laurent 1 Gillot, Valérie ...and 90 more Authors
all top 5

#### Cited in 77 Serials

 20 Journal of Number Theory 17 Finite Fields and their Applications 13 Advances in Mathematics 10 Transactions of the American Mathematical Society 9 Duke Mathematical Journal 7 Inventiones Mathematicae 7 Proceedings of the American Mathematical Society 5 Compositio Mathematica 5 Journal of Pure and Applied Algebra 5 Mathematische Annalen 4 Israel Journal of Mathematics 4 Journal of Algebra 4 Mathematische Zeitschrift 4 Revista Matemática Iberoamericana 3 Annales de l’Institut Fourier 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Journal für die Reine und Angewandte Mathematik 3 International Journal of Mathematics 3 Mémoires de la Société Mathématique de France. Nouvelle Série 3 International Journal of Number Theory 2 Discrete Applied Mathematics 2 Discrete Mathematics 2 Manuscripta Mathematica 2 Monatshefte für Mathematik 2 Nagoya Mathematical Journal 2 Rendiconti del Seminario Matematico della Università di Padova 2 Discrete & Computational Geometry 2 Bulletin of the American Mathematical Society. New Series 2 Indagationes Mathematicae. New Series 2 Cybernetics and Systems Analysis 2 Journal de Théorie des Nombres de Bordeaux 2 Kyushu Journal of Mathematics 2 The Ramanujan Journal 2 LMS Journal of Computation and Mathematics 2 Science China. Mathematics 1 Bulletin of the Australian Mathematical Society 1 Communications in Mathematical Physics 1 Beiträge zur Algebra und Geometrie 1 Archiv der Mathematik 1 Czechoslovak Mathematical Journal 1 Glasgow Mathematical Journal 1 Illinois Journal of Mathematics 1 Journal of Combinatorial Theory. Series A 1 Journal of Computational and Applied Mathematics 1 Journal of the London Mathematical Society. Second Series 1 The Journal of Symbolic Logic 1 Mathematika 1 Michigan Mathematical Journal 1 Pacific Journal of Mathematics 1 Proceedings of the Japan Academy. Series A 1 Proceedings of the London Mathematical Society. Third Series 1 Programming and Computer Software 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Results in Mathematics 1 Theoretical Computer Science 1 Tohoku Mathematical Journal. Second Series 1 Annals of Global Analysis and Geometry 1 Journal of Symbolic Computation 1 Journal of Complexity 1 Journal of the American Mathematical Society 1 Forum Mathematicum 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Journal of Algebraic Geometry 1 Selecta Mathematica. New Series 1 Sbornik: Mathematics 1 Journal of the European Mathematical Society (JEMS) 1 Acta Mathematica Sinica. English Series 1 Journal of Dynamical and Control Systems 1 Journal of High Energy Physics 1 Integers 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Central European Journal of Mathematics 1 Journal of the Institute of Mathematics of Jussieu 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Algebra & Number Theory 1 Cryptography and Communications 1 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications
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#### Cited in 29 Fields

 130 Algebraic geometry (14-XX) 115 Number theory (11-XX) 54 Special functions (33-XX) 35 Several complex variables and analytic spaces (32-XX) 26 Commutative algebra (13-XX) 11 Convex and discrete geometry (52-XX) 9 Field theory and polynomials (12-XX) 9 Associative rings and algebras (16-XX) 8 Partial differential equations (35-XX) 7 Combinatorics (05-XX) 7 Group theory and generalizations (20-XX) 5 Ordinary differential equations (34-XX) 5 Differential geometry (53-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Functional analysis (46-XX) 3 Computer science (68-XX) 2 Mathematical logic and foundations (03-XX) 2 $$K$$-theory (19-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Operations research, mathematical programming (90-XX) 2 Information and communication theory, circuits (94-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Category theory; homological algebra (18-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Operator theory (47-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX) 1 Quantum theory (81-XX)