Elementary Theory of L-functions and Eisenstein Series

An elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise.

Haruzo Hida (Author)

9780521435697, Cambridge University Press

Paperback, published 11 February 1993

400 pages
22.8 x 15.1 x 2 cm, 0.571 kg

"...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

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.

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.

Subject Areas: Number theory [PBH]