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El. knyga: Elementary Theory of L-functions and Eisenstein Series

(University of California, Los Angeles)
Kitos knygos pagal šią temą:
Elementary Theory of L-functions and Eisenstein SeriesDidesnis paveikslėlis
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An elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise.

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.

Recenzijos

"...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

Daugiau informacijos

An elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise.
1. Algebraic number theory
2. Classical L-functions and Eisenstein series
3. p-adic Hecke L-functions
4. Homological interpretation
5. Elliptical modular forms and their L-functions
6. Modular forms and cohomology groups
7. Ordinary L-adic forms, two-variable p-adic Rankin products and Galois representations
8. Functional equations of Hecke L-functions
9. Adelic Eisenstein series and Rankin products
10. Three-variable p-adic Rankin products.
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