Editors:
Brings together contributions from diverse areas, exposing users of Eisenstein series to a variety of important applications
Focuses on the common structural properties of Eisenstein series as applied to several recent developments in arithmetic: Arakelov intersection theory on Shimura varieties, special values of L-functions and Iwasawa theory, and equidistribution of rational/integer points on homogeneous varieties
Includes supplementary material: sn.pub/extras
Part of the book series: Progress in Mathematics (PM, volume 258)
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Table of contents (11 chapters)
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Front Matter
About this book
Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas that are not usually interacting with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series.
The central theme of the exposition focuses on the common structural properties of Eisenstein series occurring in many related applications that have arisen in several recent developments in arithmetic: Arakelov intersection theory on Shimura varieties, special values of L-functions and Iwasawa theory, and equidistribution of rational/integer points on homogeneous varieties. Key questions that are considered include: Is it possible to identify a class of Eisenstein series whose Fourier coefficients (resp. special values) encode significant arithmetic information? Do such series fit into p-adic families? Are the Eisenstein series that arise in counting problems of this type?
Editors and Affiliations
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Department of Mathematics, University of California, San Diego, La Jolla, USA
Wee Teck Gan
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Department of Mathematics, University of Toronto, Toronto, Canada
Stephen S. Kudla
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Courant Institute of Mathematical Sciences, New York University, New York, USA
Yuri Tschinkel
Bibliographic Information
Book Title: Eisenstein Series and Applications
Editors: Wee Teck Gan, Stephen S. Kudla, Yuri Tschinkel
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-0-8176-4639-4
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2008
Hardcover ISBN: 978-0-8176-4496-3Published: 18 January 2008
eBook ISBN: 978-0-8176-4639-4Published: 22 December 2007
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: X, 314
Topics: Number Theory, Applications of Mathematics, Geometry, Algebraic Geometry, Topological Groups, Lie Groups