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Elementary Theory of L-functions and Eisenstein Series : London Mathematical Society Student Texts - Haruzo Hida

Elementary Theory of L-functions and Eisenstein Series

London Mathematical Society Student Texts

Hardcover Published: 26th February 1993
ISBN: 9780521434119
Number Of Pages: 400

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This book is a comprehensive and systematic account of the theory of p-adic and classical modular forms and the theory of the special values of arithmetic L-functions and p-adic L-functions. The approach is basically algebraic, and the treatment is elementary. No deep knowledge from algebraic geometry and representation theory is required. The author's main tool in dealing with these problems is taken from cohomology theory over Riemann surfaces, which is also explained in detail in the book. He also gives a concise but thorough treatment of analytic continuation and functional equation. Graduate students wishing to know more about L-functions will find this a unique introduction to this fascinating branch of mathematics.

"...its style is unusually lively; even in the exposition of classical results, one feels that the proof has been reinvented and is often illuminating...a large part of the text explains theories and results due to the author; behind a classical title are hidden many theorems never published in book form until now...one must be thankful to the author to have written down the first accessible presentation of the various aspects of his theory...highly reommended to graduate students and more advanced researchers wishing to learn this powerful theory." Jacques Tilouine, Mathematical Reviews "...this is a comprehensive and important book-one that deserves to be studied carefully by any serious student of L-functions and modular forms." Glen Stevens,Bulletin of the American Mathematical Society

Suggestions to the reader
Algebraic number theory
Classical L-functions and Eisenstein series
p-adic Hecke L-functions
Homological interpretation
Elliptical modular forms and their L-functions
Modular forms and cohomology groups
Ordinary L-adic forms, two-variable p-adic Rankin products and Galois representations
Functional equations of Hecke L-functions
Adelic Eisenstein series and Rankin products
Three-variable p-adic Rankin products
Answers to selected exercises
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521434119
ISBN-10: 0521434114
Series: London Mathematical Society Student Texts
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 400
Published: 26th February 1993
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 2.5
Weight (kg): 0.76