Dwork, Bernard M.
Overview
Works:  23 works in 87 publications in 3 languages and 1,718 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Dedicatee, Editor, Honoree 
Classifications:  QA564, 516.35 
Publication Timeline
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Most widely held works about
Bernard M Dwork
 On a theorem of Dwork by Benjamin Michael Dickman( Book )
Most widely held works by
Bernard M Dwork
Padic analysis : proceedings of the international conference held in Trento, Italy, May 29June 2, 1989 by Francesco Baldassari(
Book
)
14 editions published in 1990 in English and German and held by 483 WorldCat member libraries worldwide
14 editions published in 1990 in English and German and held by 483 WorldCat member libraries worldwide
Lectures on padic differential equations by
Bernard M Dwork(
Book
)
14 editions published between 1980 and 1982 in English and held by 433 WorldCat member libraries worldwide
14 editions published between 1980 and 1982 in English and held by 433 WorldCat member libraries worldwide
An introduction to Gfunctions by
Bernard M Dwork(
Book
)
9 editions published in 1994 in English and held by 357 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
9 editions published in 1994 in English and held by 357 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
)
8 editions published in 1990 in English and Undetermined and held by 311 WorldCat member libraries worldwide
8 editions published in 1990 in English and Undetermined and held by 311 WorldCat member libraries worldwide
On the zeta function of a hypersurface by
Bernard M Dwork(
Book
)
11 editions published in 1962 in English and French and held by 68 WorldCat member libraries worldwide
11 editions published in 1962 in English and French and held by 68 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 Undetermined and held by 15 WorldCat member libraries worldwide
5 editions published in 1969 in English and Undetermined 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 7 WorldCat member libraries worldwide
3 editions published in 1954 in English and held by 7 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 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(
Book
)
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
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
padic analysis : International conference : Papers(
)
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
1 edition published in 1990 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
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
Operators with nilpotentpcurvature by Hans Lothar Schmitt(
Book
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
We consider linear ordinary differential operators $L\in\Re=Im(x)\left({d\over dx}\right),$ where Im is a field of characteristic p. Such an operator of order n is said to have nilpotent pcurvature if $D\sp{pn}\in\Re L.$ Fixing the order n and the number $m+1$ of singularities on the sphere and the exponents, such an operator is parametrized by the singularities and the accessory parameters. It was previously shown by Dwork ( (Dw,1)) that the algebraic set defined by the condition that L be nilpotent is of dimension bounded by $m  2;$ furthermore, in the case of $n=2$ it was shown that the algebraic set is a complete intersection which is nonempty. We extend this result to arbitrary order by counting the number of conditions and by showing the algebraic set to be nonempty for any choice of exponents lying in ${\bf F\sb{p}}$ and satisfying Fuchs' condition
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
We consider linear ordinary differential operators $L\in\Re=Im(x)\left({d\over dx}\right),$ where Im is a field of characteristic p. Such an operator of order n is said to have nilpotent pcurvature if $D\sp{pn}\in\Re L.$ Fixing the order n and the number $m+1$ of singularities on the sphere and the exponents, such an operator is parametrized by the singularities and the accessory parameters. It was previously shown by Dwork ( (Dw,1)) that the algebraic set defined by the condition that L be nilpotent is of dimension bounded by $m  2;$ furthermore, in the case of $n=2$ it was shown that the algebraic set is a complete intersection which is nonempty. We extend this result to arbitrary order by counting the number of conditions and by showing the algebraic set to be nonempty for any choice of exponents lying in ${\bf F\sb{p}}$ and satisfying Fuchs' condition
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Audience Level
0 

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Related Identities
 Bosch, S. (Siegfried) 1944 Editor
 Baldassarri, F. (Francesco) 1951 Editor
 Centro internazionale per la ricerca matematica (Trento, Italy)
 Gerotto, Giovanni
 Sullivan, Francis J. 1943
 SpringerLink (Service en ligne)
 Serre, JeanPierre
 Atiyah, Michael Francis Author
 Singer, I.M. (Isadore Manuel) Mathematiker 1924
 Baldassari, Francesco Author
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