Six Short Chapters on Automorphic Forms and L-functions

✍ Scribed by Ze-Li Dou, Qiao Zhang (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2012
• Tongue: English
• Leaves: 130
• Edition: 1
• Category: Library

✦ Synopsis

"Six Short Chapters on Automorphic Forms and L-functions" treats the period conjectures of Shimura and the moment conjecture. These conjectures are of central importance in contemporary number theory, but have hitherto remained little discussed in expository form. The book is divided into six short and relatively independent chapters, each with its own theme, and presents a motivated and lively account of the main topics, providing professionals an overall view of the conjectures and providing researchers intending to specialize in the area a guide to the relevant literature.

Ze-Li Dou and Qiao Zhang are both associate professors of Mathematics at Texas Christian University, USA.

✦ Table of Contents

Front Matter....Pages i-xi
Modular forms and the Shimura-Taniyama Conjecture....Pages 1-16
Periods of automorphic forms....Pages 17-42
Lifting of automorphic forms....Pages 43-55
Zeros of L -functions....Pages 57-75
Special Values of L -functions....Pages 77-98
Theta lifts and periods with respect to a quadratic extension....Pages 99-123

✦ Subjects

Number Theory; Algebraic Geometry