L-Functions and Arithmetic

doi:10.1017/CBO9780511526053

This volume is an outgrowth of the LMS Durham Symposium on L-functions, held in July 1989. The symposium consisted of several short courses, aimed at presenting rigorous but non-technical expositions of the latest research areas, and a number of individual lectures on specific topics. The contributors are all outstanding figures in the area of algebraic number theory and this volume will be of lasting value to students and researchers working in the area.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-vii
- By J. Coates, University of Cambridge, M. J. Taylor, University of Manchester Institute of Science and Technology
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Participants
pp viii-viii
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Lectures on automorphic L-functions
pp 1-60
- By James Arthur, Stephen Gelbart
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Gauss sums and local constants for GL(N)
pp 61-74
- By Colin J. Bushnell
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L-functions and Galois modules
pp 75-140
- By PH. Cassou-Noguès, T. Chinburg, A. Fröhlich, M. J. Taylor, D. Burns, N. P. Byott
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Motivic p-adic L-functions
pp 141-172
- By John Coates
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The Beilinson conjectures
pp 173-210
- By Christopher Deninger, Anthony J. Scholl
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Iwasawa theory for motives
pp 211-234
- By Ralph Greenberg
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Kolyvagin's work for modular elliptic curves
pp 235-256
- By Benedict H. Gross
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Index theory, potential theory, and the Riemann hypothesis
pp 257-270
- By Shai Haran
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Katz p-adic L-functions, congruence modules and deformation of Galois representations
pp 271-294
- By H. Hida, J. Tilouine
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Kolyvagin's work on Shafarevich-Tate groups
pp 295-316
- By William G. McCallum
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Arithmetic of diagonal quartic surfaces I
pp 317-338
- By R.G.E. Pinch, H.P.F. Swinnerton-Dyer
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On certain Artin L-Series
pp 339-352
- By Dinakar Ramakrishnan
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The one-variable main conjecture for elliptic curves with complex multiplication
pp 353-372
- By Karl Rubin, Department of Mathematics, Ohio State University, Columbus, OH 43210, USA
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Remarks on special values of L-functions
pp 373-392
- By Anthony J. Scholl
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L-Functions and Arithmetic

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-vii

Participants
pp viii-viii

Lectures on automorphic L-functions
pp 1-60

Gauss sums and local constants for GL(N)
pp 61-74

L-functions and Galois modules
pp 75-140

Motivic p-adic L-functions
pp 141-172

The Beilinson conjectures
pp 173-210

Iwasawa theory for motives
pp 211-234

Kolyvagin's work for modular elliptic curves
pp 235-256

Index theory, potential theory, and the Riemann hypothesis
pp 257-270

Katz p-adic L-functions, congruence modules and deformation of Galois representations
pp 271-294

Kolyvagin's work on Shafarevich-Tate groups
pp 295-316

Arithmetic of diagonal quartic surfaces I
pp 317-338

On certain Artin L-Series
pp 339-352

The one-variable main conjecture for elliptic curves with complex multiplication
pp 353-372

Remarks on special values of L-functions
pp 373-392

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L-Functions and Arithmetic

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