Gauss Sums, Kloosterman Sums, and Monodromy Groups by Nicholas M. Katz
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Gauss Sums, Kloosterman Sums, and Monodromy Groups
By Nicholas M. Katz

Gauss Sums, Kloosterman Sums, and Monodromy Groups

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Format: Paperback

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Gauss Sums, Kloosterman Sums, and Monodromy Groups by Nicholas M. Katz

Book Description

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 work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.

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Book Details

ISBN: 9780691084336
ISBN-10: 0691084335
Format: Paperback
(235mm x 155mm x 15mm)
Pages: 256
Imprint: Princeton University Press
Publisher: Princeton University Press
Publish Date: 1-Aug-1988
Country of Publication: United States

Books By Author Nicholas M. Katz

Convolution and Equidistribution by Nicholas M. Katz Convolution and Equidistribution, Paperback (January 2012)

Explores an important aspect of number theory - the theory of exponential sums over finite fields and their Mellin transforms - from a categorical point of view. This book presents fundamentally important results and a plethora of examples, opening up new directions in the subject.

Moments, Monodromy, and Perversity by Nicholas M. Katz Moments, Monodromy, and Perversity, Paperback (September 2005)

Develops techniques based on two ingredients: the theory of perverse sheaves and Larsen's Alternative. These techniques are then used to calculate the geometric monodromy groups attached to some specific universal families of (L-functions attached to) character sums over finite fields.

Twisted L-Functions and Monodromy by Nicholas M. Katz Twisted L-Functions and Monodromy, Paperback (February 2002)

For hundreds of years, the study of elliptic curves has played a central role in mathematics. This book explores: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? It is suitable for those interested in number theory and algebraic geometry.

Rigid Local Systems by Nicholas M. Katz Rigid Local Systems, Paperback (December 1995)

The author 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 systems (of local holomorphic solutions) to which they gave rise.

» View all books by Nicholas M. Katz

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Recent books by Nicholas M. Katz close
Convolution and Equidistribution by Nicholas M. Katz
Moments, Monodromy, and Perversity by Nicholas M. Katz
Twisted L-Functions and Monodromy by Nicholas M. Katz
Rigid Local Systems by Nicholas M. Katz
Exponential Sums and Differential Equations by Nicholas M. Katz
Arithmetic Moduli of Elliptic Curves by Nicholas M. Katz
»
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