Bernard Dwork

Q: What Schools Are Affiliated With Bernard Dwork

Bernard Dwork is affiliated with the following schools: City College of New York, Princeton University, Purdue University, Columbia University

Bernard Dwork's AcademicInfluence.com Rankings

Bernard Dwork

Mathematics

#503

World Rank

#980

Historical Rank

#228

USA Rank

Measure Theory

#2067

World Rank

#2504

Historical Rank

#607

USA Rank

mathematics Degrees

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Mathematics

Why Is Bernard Dwork Influential?

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According to Wikipedia, Bernard Morris Dwork was an American mathematician, known for his application of p-adic analysis to local zeta functions, and in particular for a proof of the first part of the Weil conjectures: the rationality of the zeta-function of a variety over a finite field. The general theme of Dwork's research was p-adic cohomology and p-adic differential equations. He published two papers under the pseudonym Maurizio Boyarsky.

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Bernard Dwork's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Generalized Hypergeometric Functions (1990) (1068)
On the Rationality of the Zeta Function of an Algebraic Variety (1960) (386)
On the zeta function of a hypersurface (1962) (266)
An introduction to G-functions (1994) (189)
Exponential sums and Newton polyhedra: Cohomology and estimates (1989) (166)
p-adic cycles (1969) (146)
On the Zeta Function of a Hypersurface: III (1964) (134)
On Second Order Linear Differential Equations with Algebraic Solutions (1979) (101)
Lectures on p-adic Differential Equations (1982) (80)
Normalized period matrices II (1973) (75)
Bessel functions as $p$-adic functions of the argument (1974) (56)
p-adic Analysis (1990) (56)
Detection of a Pulse Superimposed on Fluctuation Noise (1950) (45)
Measurement of flow in straight tubes by means of the dilution technique. (1953) (44)
Norm residue Symbol in local number Fields (1958) (42)
On P-Adic Differential Equations. III. On P-Adically Bounded Solutions of Ordinary Linear Differential Equations with Rational Function Coefficients. (1973) (38)
On ordinary linear $p$-adic differential equations (1977) (35)
On natural radii of $p$-adic convergence (1979) (35)
On the mod p 2 determination of ((p-1)/2 (p-1)/4) (1986) (34)
On $p$-adic differential equations IV generalized hypergeometric functions as $p$-adic analytic functions in one variable (1973) (34)
Differential Operators with Nilpotent p-Curvature (1990) (31)
On Hecke polynomials (1971) (30)
The Eisenstein constant (1992) (30)
On the mod p2 determination of ((p − 1)4(p − 1)2) (1986) (30)
Canonical liftings of jacobians (1986) (29)
On the Artin Root Number (1956) (27)
On p-Adic Differential Equations II: The p-Adic Asymptotic Behavior of Solutions of Ordinary Linear Differential Equations with Rational Function Coefficients (1973) (25)
Logarithmic decay and overconvergence of the unit root and associated zeta functions (1991) (24)
Normalized Period Matrices I: Plane Curves (1971) (21)
Effective $p$-adic bounds at regular singular points (1991) (20)
An Introduction to G-Functions. (AM-133), Volume 133 (1994) (20)
Effective $p$-adic bounds for solutions of homogeneous linear differential equations (1980) (19)
On exponents of p-adic differential modules. (1997) (17)
A note on the $p$-adic gamma function (1982) (14)
On Kummer’s twenty-four solutions of the hypergeometric differential equation (1984) (13)
On the Zeta Function of a Hypersurface: IV. A Deformation Theory for Singular Hypersurfaces (1969) (11)
On the Uniqueness of Frobenius Operator on Differential Equations (1989) (10)
ON THE BOYARSKY PRINCIPLE (1983) (10)
The Up operator of Atkin on modular functions of level 2 with growth conditions (1973) (9)
On $p$-adic differential equations. The Frobenius structure of differential equations (1974) (9)
Corrections to “The Eisenstein constant” (1994) (8)
On the Rationality of Zeta Functions and L-Series (1967) (7)
On the congruence properties of the zeta function of algebraic varieties. (1960) (6)
On the Tate constant (1984) (6)
On Apery's differential operator (1981) (6)
ON THE SIZE OF DIFFERENTIAL MODULES (1999) (5)
Growth of solutions of linear differential equations at a logarithmic singularity (1982) (4)
Cohomological interpretation of hypergeometric series (1993) (3)
Contiguity relations for generalized hypergeometric functions (1995) (3)
Hypergeometric Series and Functions as Periods of Exponential Modules (1994) (2)
On Systems of Ordinary Differential Equations with Transcendental Parameters (1999) (2)
Differential equations which come from geometry (1982) (2)
p-adic Gamma Functions (1982) (2)
On ordinary linear $p$-adic differential equations with algebraic function coefficients (1976) (2)
Majoration effective et application (1982) (1)
Cohomology of singular hypersurfaces (2000) (1)
PHOTOFLUORIMETERS FOR DETERMINATION OF URANIUM AND BERYLLIUM CONCENTRATIONS (1954) (1)
APPENDIX III. CAUCHY'S THEOREM (1994) (0)
APPENDIX II. ARCHIMEDEAN ESTIMATES (1994) (0)
On singular projective structures on Riemann Surfaces (1989) (0)
CHAPTER VIII. G-SERIES. THE THEOREM OF CHUDNOVSKY (1994) (0)
LIST OF SYMBOLS (1994) (0)
The Space L (Algebraic Theory) (1982) (0)
Dual Theory (Algebraic) (1982) (0)
Analytic Dual Theory (1982) (0)
P-adic analysis : proceedings of the international conference held in Trento, Italy, May 29-June 2, 1989 (1990) (0)
APPENDIX I. CONVERGENCE POLYGON FOR DIFFERENTIAL EQUATIONS (1994) (0)
Basic Properties of ψ Operator (1982) (0)
Normalized Solution Matrix (1982) (0)
CHAPTER IV. EFFECTIVE BOUNDS. ORDINARY DISKS (1994) (0)
Second-Order Linear Differential Equations Modulo Powers of p (1982) (0)
Singular residue classes which are ordinary for $F(a,\,b,\,c,\,\lambda )$ (1982) (0)
The Function τ on Supersingular Disks (l = 1) (1982) (0)
CHAPTER VI. TRANSFER THEOREMS INTO DISKS WITH ONE SINGULARITY (1994) (0)
p-adic Beta Functions (1982) (0)
Singular Disks, Part I (1982) (0)
Beta Function as Residues (1982) (0)
On the mod p2 Determination of (ig-:jG) (2003) (0)
The a → a′ Map (1982) (0)
CHAPTER I. VALUED FIELDS (1994) (0)
Nilpotent Second-Order Linear Differential Equations with Fuchsian Singularities (1982) (0)
Analytic Factors of Power Series (1982) (0)
The Defining Relation for the Canonical Lifting (l = 1) (1982) (0)
OnP-adic differential equations (1973) (0)
Singular Disks, Part II. Nonlogarithmic Case (1982) (0)
Applications of Analysis to Algebraic Geometry. (1971) (0)
CHAPTER VII. DIFFERENTIAL EQUATIONS OF ARITHMETIC TYPE (1994) (0)
CHAPTER II. ZETA FUNCTIONS (1994) (0)
Calculation Modulo p of the Matrix of α f,h (1982) (0)
CHAPTER V. EFFECTIVE BOUNDS. SINGULAR DISKS (1994) (0)
THE LOCAL STRUCTURE OF THE ARTIN ROOT NUMBER. (1955) (0)
Canonical Liftings (l ≥ 1) (1982) (0)
Canonical Lifting for l = 1 (1982) (0)
CHAPTER III. DIFFERENTIAL EQUATIONS (1994) (0)
Work of Philippe Robba (1990) (0)

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What Schools Are Affiliated With Bernard Dwork?

Bernard Dwork is affiliated with the following schools: