Introduction to Modular Forms

✍ Scribed by Serge Lang (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1987
• Tongue: English
• Leaves: 269
• Series: Grundlehren der mathematischen Wissenschaften 222
• Edition: 1
• Category: Library

✦ Synopsis

From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given... In conclusion, this book is a welcome addition to the literature for the growing number of students and mathematicians in other fields who want to understand the recent developments in the theory of modular forms."
#Mathematical Reviews#
"This book will certainly be indispensable to all those wishing to get an up-to-date initiation to the theory of modular forms."
#Publicationes Mathematicae#

✦ Table of Contents

Front Matter....Pages i-ix
Front Matter....Pages 1-1
Modular Forms....Pages 3-15
Hecke Operators....Pages 16-23
The Petersson Scalar Product....Pages 24-43
Front Matter....Pages N1-N1
Modular Symbols....Pages 57-67
Coefficients and Periods of Cusp Forms on SL 2 ( Z )....Pages 68-83
The Eichler-Shimura Isomorphism on SL 2 ( Z )....Pages 84-98
Front Matter....Pages 99-99
Higher Levels....Pages 101-117
Atkin-Lehner Theory....Pages 118-137
The Dedekind Formalism....Pages 138-147
Front Matter....Pages 149-149
Congruences and Reduction mod p ....Pages 151-175
Galois Representations....Pages 176-203
Front Matter....Pages 205-205
General Distributions....Pages 207-227
Bernoulli Numbers and Polynomials....Pages 228-239
The Complex L -Functions....Pages 240-246
The Hecke-Eisenstein and Klein Forms....Pages 247-254
Back Matter....Pages 255-264

✦ Subjects

Number Theory; Analysis; Algebraic Geometry