Nicholas M. Katz is Professor of Mathematics at Princeton University. He is the author of four other books in this series:
Arithmetic Moduli of Elliptic Curves (with Barry Mazur);
Gauss Sums, Kloosterman Sums, and Monodromy Groups; Exponential Sums and Differential Equations; and
Rigid Local Systems.
11 द्वारा ईबुक Nicholas M. Katz
Nicholas M. Katz: Twisted L-Functions and Monodromy
For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell’s theorem in 1922 to th …
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Nicholas M. Katz: Moments, Monodromy, and Perversity
It is now some thirty years since Deligne first proved his general equidistribution theorem, thus establishing the fundamental result governing the statistical properties of suitably ‘pure’ algebro-g …
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Nicholas M. Katz: Convolution and Equidistribution
Convolution and Equidistribution explores an important aspect of number theory–the theory of exponential sums over finite fields and their Mellin transforms–from a new, categorical point of view. T …
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Nicholas M. Katz & Barry Mazur: Arithmetic Moduli of Elliptic Curves
This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi’s ‘Fundamenta Nova’ …
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Nicholas M. Katz: Gauss Sums, Kloosterman Sums, and Monodromy Groups
The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne’s …
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Nicholas M. Katz: Exponential Sums and Differential Equations
This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equation …
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Nicholas M. Katz: Rigid Local Systems
Riemann introduced the concept of a ‘local system’ on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local syst …
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Nicholas M. Katz & Pham Huu Tiep: Exponential Sums, Hypergeometric Sheaves, and Monodromy Groups
An examination of some of the remarkable connections between group theory and arithmetic algebraic geometry over finite fields Exponential sums have been of great interest ever since Gauss, and their …
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