Dwork, Bernard M.
Overview
Works:  20 works in 106 publications in 3 languages and 1,892 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Dedicatee, Honoree, Other 
Classifications:  QA372, 515.35 
Publication Timeline
.
Most widely held works by
Bernard M Dwork
Lectures on padic differential equations by
Bernard M Dwork(
Book
)
19 editions published between 1980 and 2011 in English and held by 423 WorldCat member libraries worldwide
The present work treats padic properties of solutions of the hypergeometric differential equation d2 d ~ (x(l  x) dx + (c(l  x) + (c  1  a  b)x) dx  ab)y = 0, 2 with a, b, c in 4) n Zp, by constructing the associated Frobenius structure. For this construction we draw upon the methods of Alan Adolphson [1] in his 1976 work on Hecke polynomials. We are also indebted to him for the account (appearing as an appendix) of the relation between this differential equation and certain Lfunctions. We are indebted to G. Washnitzer for the method used in the construction of our dual theory (Chapter 2). These notes represent an expanded form of lectures given at the U.L.P. in Strasbourg during the fall term of 1980. We take this opportunity to thank Professor R. Girard and IRMA for their hospitality. Our subjectpadic analysiswas founded by Marc Krasner. We take pleasure in dedicating this work to him. Contents 1 Introduction ... 1. The Space L (Algebraic Theory) 8 2. Dual Theory (Algebraic) 14 3. Transcendental Theory ... 33 4. Analytic Dual Theory. ... 48 5. Basic Properties of", Operator. 73 6. Calculation Modulo p of the Matrix of ~ f, h 92 7. Hasse Invariants ... 108 8. The a + a' Map ... 110 9. Normalized Solution Matrix. ... 113 10. Nilpotent SecondOrder Linear Differential Equations with Fuchsian Singularities. ... 137 11. SecondOrder Linear Differential Equations Modulo Powers ofp
19 editions published between 1980 and 2011 in English and held by 423 WorldCat member libraries worldwide
The present work treats padic properties of solutions of the hypergeometric differential equation d2 d ~ (x(l  x) dx + (c(l  x) + (c  1  a  b)x) dx  ab)y = 0, 2 with a, b, c in 4) n Zp, by constructing the associated Frobenius structure. For this construction we draw upon the methods of Alan Adolphson [1] in his 1976 work on Hecke polynomials. We are also indebted to him for the account (appearing as an appendix) of the relation between this differential equation and certain Lfunctions. We are indebted to G. Washnitzer for the method used in the construction of our dual theory (Chapter 2). These notes represent an expanded form of lectures given at the U.L.P. in Strasbourg during the fall term of 1980. We take this opportunity to thank Professor R. Girard and IRMA for their hospitality. Our subjectpadic analysiswas founded by Marc Krasner. We take pleasure in dedicating this work to him. Contents 1 Introduction ... 1. The Space L (Algebraic Theory) 8 2. Dual Theory (Algebraic) 14 3. Transcendental Theory ... 33 4. Analytic Dual Theory. ... 48 5. Basic Properties of", Operator. 73 6. Calculation Modulo p of the Matrix of ~ f, h 92 7. Hasse Invariants ... 108 8. The a + a' Map ... 110 9. Normalized Solution Matrix. ... 113 10. Nilpotent SecondOrder Linear Differential Equations with Fuchsian Singularities. ... 137 11. SecondOrder Linear Differential Equations Modulo Powers ofp
Padic analysis : proceedings of the international conference held in Trento, Italy, May 29June 2, 1989 by
F Baldassarri(
Book
)
19 editions published in 1990 in English and German and held by 371 WorldCat member libraries worldwide
19 editions published in 1990 in English and German and held by 371 WorldCat member libraries worldwide
An introduction to Gfunctions by
Bernard M Dwork(
Book
)
11 editions published in 1994 in English and held by 363 WorldCat member libraries worldwide
After presenting a review of valuation theory and elementary padic analysis together with an application to the congruence zeta function, this book offers a detailed study of the padic properties of formal power series solutions of linear differential equations. In particular, the padic radii of convergence and the padic growth of coefficients are studied. Recent work of Christol, Bombieri, André, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G series is again a G series. This book will be indispensable for those wishing to study the work of Bombieri and André on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations
11 editions published in 1994 in English and held by 363 WorldCat member libraries worldwide
After presenting a review of valuation theory and elementary padic analysis together with an application to the congruence zeta function, this book offers a detailed study of the padic properties of formal power series solutions of linear differential equations. In particular, the padic radii of convergence and the padic growth of coefficients are studied. Recent work of Christol, Bombieri, André, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G series is again a G series. This book will be indispensable for those wishing to study the work of Bombieri and André on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations
Generalized hypergeometric functions by
Bernard M Dwork(
Book
)
13 editions published between 1990 and 2011 in English and Undetermined and held by 309 WorldCat member libraries worldwide
13 editions published between 1990 and 2011 in English and Undetermined and held by 309 WorldCat member libraries worldwide
On the zeta function of a hypersurface by
Bernard M Dwork(
Book
)
14 editions published in 1962 in English and French and held by 71 WorldCat member libraries worldwide
This article is concerned with the further development of the methods of padic analysis used in an earlier article to study the zeta function of an algebraic variety defined over a finite field. These methods are applied to the zeta function of a nonsingular hypersurface of degree d in projective nspace of characteristic p defined over the field of q elements
14 editions published in 1962 in English and French and held by 71 WorldCat member libraries worldwide
This article is concerned with the further development of the methods of padic analysis used in an earlier article to study the zeta function of an algebraic variety defined over a finite field. These methods are applied to the zeta function of a nonsingular hypersurface of degree d in projective nspace of characteristic p defined over the field of q elements
Cohomologie padique by
Bernard M Dwork(
Book
)
8 editions published in 1984 in French and English and held by 24 WorldCat member libraries worldwide
8 editions published in 1984 in French and English and held by 24 WorldCat member libraries worldwide
Index theory for skewadjoint Fredholm operators by
Michael Francis Atiyah(
Book
)
7 editions published in 1969 in English and held by 21 WorldCat member libraries worldwide
7 editions published in 1969 in English and held by 21 WorldCat member libraries worldwide
Photofluorimeters for determination of uranium and beryllium concentrations by H. J DiGiovanni(
Book
)
3 editions published in 1954 in English and held by 10 WorldCat member libraries worldwide
3 editions published in 1954 in English and held by 10 WorldCat member libraries worldwide
On the zeta function of a hypersurface (p. 5 à 68) by
Bernard M Dwork(
Book
)
1 edition published in 1962 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1962 in English and held by 3 WorldCat member libraries worldwide
On the zeta function of a hypersurface by
Bernard M Dwork(
)
1 edition published in 1962 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1962 in English and held by 2 WorldCat member libraries worldwide
On the root number in the functional equation of the ArtinWeil Lseries by
Bernard M Dwork(
)
1 edition published in 1954 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1954 in English and held by 2 WorldCat member libraries worldwide
An introduction fo Gfunctions : Bernard Dwork, Giovanni Gerotto, Francis J. Sullivan by
Bernard M Dwork(
Book
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
Applications of Analysis to Algebraic Geometry(
Book
)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
A project concerned with enumerative geometry is briefly summarized. (Author)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
A project concerned with enumerative geometry is briefly summarized. (Author)
Lectures on topics on Diophantine approximation given in the Summer of 1950 by
Harold N Shapiro(
Book
)
in English and held by 1 WorldCat member library worldwide
in English and held by 1 WorldCat member library worldwide
PAdic cycles by
Bernard M Dwork(
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
Geometric aspects of Dwork theory(
Book
)
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
This twovolume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923  1998). It presents a wideranging overview of some of the most active areas of contemporary research in arithmetic algebraic geometry, with special emphasis on the geometric applications of the padic analytic techniques originating in Dwork's work, their connection to various recent cohomology theories and to modular forms. The two volumes contain both important new research and illuminating survey article
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
This twovolume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923  1998). It presents a wideranging overview of some of the most active areas of contemporary research in arithmetic algebraic geometry, with special emphasis on the geometric applications of the padic analytic techniques originating in Dwork's work, their connection to various recent cohomology theories and to modular forms. The two volumes contain both important new research and illuminating survey article
An Introduction to "G"Functions. (AM133) by
Bernard M Dwork(
)
1 edition published in 2016 in English and held by 0 WorldCat member libraries worldwide
Written for advanced undergraduate and firstyear graduate students, this book aims to introduce students to a serious level of padic analysis with important implications for number theory. The main object is the study of Gseries, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K. These series satisfy a linear differential equation Ly=0 with LIK(x) [d/dx] and have nonzero radii of convergence for each imbedding of K into the complex numbers. They have the further property that the common denominators of the first s coefficients go to infinity geometrically with the index s. After presenting a review of valuation theory and elementary padic analysis together with an application to the congruence zeta function, this book offers a detailed study of the padic properties of formal power series solutions of linear differential equations. In particular, the padic radii of convergence and the padic growth of coefficients are studied. Recent work of Christol, Bombieri, André, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G series is again a G series. This book will be indispensable for those wishing to study the work of Bombieri and André on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations
1 edition published in 2016 in English and held by 0 WorldCat member libraries worldwide
Written for advanced undergraduate and firstyear graduate students, this book aims to introduce students to a serious level of padic analysis with important implications for number theory. The main object is the study of Gseries, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K. These series satisfy a linear differential equation Ly=0 with LIK(x) [d/dx] and have nonzero radii of convergence for each imbedding of K into the complex numbers. They have the further property that the common denominators of the first s coefficients go to infinity geometrically with the index s. After presenting a review of valuation theory and elementary padic analysis together with an application to the congruence zeta function, this book offers a detailed study of the padic properties of formal power series solutions of linear differential equations. In particular, the padic radii of convergence and the padic growth of coefficients are studied. Recent work of Christol, Bombieri, André, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G series is again a G series. This book will be indispensable for those wishing to study the work of Bombieri and André on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations
An Introduction to G Functions. (AM133) by
Bernard M Dwork(
)
1 edition published in 1994 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 1994 in English and held by 0 WorldCat member libraries worldwide
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Related Identities
 Bosch, S. (Siegfried) 1944 Other Editor
 Baldassarri, F. (Francesco) 1951 Other Author Editor
 Centro internazionale per la ricerca matematica (Trento, Italy)
 Sullivan, Francis J. 1943
 Gerotto, Giovanni
 Serre, JeanPierre
 Atiyah, Michael Francis Author
 Singer, Isadore Manuel (1924 ...)
 Conner, P.E. (Pierre E.)
 Smith, Larry (1942 ...)
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Associated Subjects
Analytic functions Banach spaces Beryllium Differential equations Differential topology Functions, Zeta Generalized spaces Geometry, Algebraic Global analysis (Mathematics) Hfunctions Homology theory Hypergeometric functions Hyperspace Mathematics Number theory padic analysis padic numbers Riemann surfaces Surfaces Uranium Weil conjectures
Alternative Names
Bernard Dwork Amerikaans wiskundige
Bernard Dwork amerikansk matematikar
Bernard Dwork amerikansk matematiker
Bernard Dwork matemático estadounidense
Bernard Dwork matematico statunitense
Bernard Dwork mathématicien américain
Bernard Dwork USamerikanischer Mathematiker
Bernard M. Dwork matematico statunitense
Dwork, B.
Dwork, B. 19231998
Dwork, B. (Bernard)
Dwork, Bernard.
Dwork, Bernard 19231998
Dwork, Bernard M.
Dwork Bernard M. 19231998
버나드 드워크
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