Dwork, Bernard M.
Overview
Works:  22 works in 100 publications in 3 languages and 1,795 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
)
18 editions published between 1980 and 1982 in English and held by 425 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
18 editions published between 1980 and 1982 in English and held by 425 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 376 WorldCat member libraries worldwide
19 editions published in 1990 in English and German and held by 376 WorldCat member libraries worldwide
An introduction to Gfunctions by
Bernard M Dwork(
Book
)
10 editions published in 1994 in English and held by 366 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
10 editions published in 1994 in English and held by 366 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
)
10 editions published between 1990 and 2011 in English and Undetermined and held by 304 WorldCat member libraries worldwide
10 editions published between 1990 and 2011 in English and Undetermined and held by 304 WorldCat member libraries worldwide
On the zeta function of a hypersurface by
Bernard M Dwork(
Book
)
13 editions published in 1962 in English and French and held by 69 WorldCat member libraries worldwide
13 editions published in 1962 in English and French and held by 69 WorldCat member libraries worldwide
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
)
5 editions published in 1969 in English and held by 15 WorldCat member libraries worldwide
5 editions published in 1969 in English and held by 15 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
Index theory for skew adjoint Fredholm operators. Padic cycles / by B. Dwork [u. a.] by
Michael Francis Atiyah(
Book
)
1 edition published in 1969 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 1969 in English and held by 5 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 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
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 ZETA FUNCTION OF A HYPERSURFACE(
Book
)
1 edition published in 1962 in English and held by 1 WorldCat member library 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
1 edition published in 1962 in English and held by 1 WorldCat member library 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
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 a
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 a
Lectures on topics on Diophantine approximation 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
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)
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
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
Index Theory for Skewadjoint Fredholm Operators, u.a by
Michael Francis Atiyah(
Book
)
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
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Related Identities
 Baldassarri, F. (Francesco) 1951 Other Author Editor
 Bosch, S. (Siegfried) 1944 Other Editor
 Centro internazionale per la ricerca matematica (Trento, Italy)
 Gerotto, Giovanni
 Sullivan, Francis J. 1943
 Serre, JeanPierre
 SpringerLink (Service en ligne)
 Atiyah, Michael Francis Author
 Singer, Isadore Manuel (1924....)
 Conner, Pierre Euclide (1932....)
Useful Links
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 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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