Elementary Theory of L-functions and Eisenstein Series (London Mathematical Society Student Texts, Series Number 26)

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. 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. Haruzo Hida. Includes Bibliographical References (p. [365]-370) And Index. The approach is basically algebraic and the treatment elementary in this 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.