Shimura Elementary Dirichlet Series and Modular Forms

1. Auflage 2007
ISBN: 978-0-387-72474-4
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 160 Seiten, eBook

Reihe: Springer Monographs in Mathematics

A book on any mathematical subject above textbook level is not of much value unless it contains new ideas and new perspectives. Also, the author may be encouraged to include new results, provided that they help the reader gain newinsightsandarepresentedalongwithknownoldresultsinaclearexposition. Itis with this philosophy that Iwrite this volume. The two subjects, Dirichlet series and modular forms, are traditional, but I treat them in both orthodox and unorthodox ways. However, I try to make the book accessible to those who are not familiar with such topics, by including plenty of expository material. More speci?c descriptions of the contents will be given in the Introduction. To some extent, this book has a supplementary nature to my previous book Introduction to the Arithmetic Theory of Automorphic Functions, published by Princeton University Press in 1971, though I do not write the present book with that intent. While the 1971 book grew out of my lectures in various places, the essential points of this new book have never been presented publicly or privately. I hope that it will draw an audience as large as that of the previous book.

Zielgruppe

Graduate

Autoren/Hrsg.

Shimura, Goro

Inhaltsverzeichnis

Preliminaries on Modular Forms and Dirichlet Series.- Critical Values of Dirichlet L-functions.- The Case of Imaginary Quadratic Fields and Nearly Holomorphic Modular Forms.- Eisenstein Series.- Critical Values of Dirichlet Series Associated with Imaginary Quadratic Fields.- Supplementary Results.