The theory of p-adic and classic modular forms, and the study of arithmetic and p-adic L-functions has proved to be a fruitful area of mathematics over the last decade. Professor Hida has given courses on these topics in the USA, Japan, and in France, and in this book provides the reader with an elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise, and the subject is approached using only basic tools from complex analysis and cohomology theory. Graduate students wishing to know more about L-functions will find that this book offers a unique introduction to this fascinating branch of mathematics.
Rezensionen / Stimmen
"...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
Reihe
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Maße
Höhe: 229 mm
Breite: 152 mm
Dicke: 23 mm
Gewicht
ISBN-13
978-0-521-43569-7 (9780521435697)
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Schweitzer Klassifikation
Autor*in
University of California, Los Angeles
Suggestions to the reader; 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; Appendix; References; Answers to selected exercises; Index.
