Eisenstein series and applications / Wee Teck Gan, Stephen S. Kudla, Yuri Tschinkel, editors.

Format:

Book

Contributor:

Gan, Wee Teck.

Kudla, Stephen S., 1950-

Tschinkel, Yuri.

Series:

Progress in mathematics (Boston, Mass.) ; v. 258.

Progress in mathematics ; v. 258

Language:

English

Subjects (All):

Eisenstein series.

Physical Description:

x, 314 pages ; 24 cm.

Place of Publication:

Boston, Mass. : Birkhäuser ; London : Springer [distributor], 2007.

Summary:

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 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?

Contents:

Twisted Weyl Group Multiple Dirichlet Series: The Stable Case / Ben Brubaker, Daniel Bump, Solomon Friedberg 1

A Topological Model for Some Summand of the Eisenstein Cohomology of Congruence Subgroups / Jens Franke 27

The Saito-Kurokawa Space of PGSp[subscript 4] and Its Transfer to Inner Forms / Wee Teck Gan 87

Values of Archimedean Zeta Integrals for Unitary Groups / Paul Garrett 125

A Simple Proof of Rationality of Siegel-Weil Eisenstein Series / Michael Harris 149

Residues of Eisenstein Series and Related Problems / Dihua Jiang 187

Some Extensions of the Siegel-Weil Formula / Stephen S. Kudla 205

A Remark on Eisenstein Series / Erez M. Lapid 239

Arithmetic Aspects of the Theta Correspondence and Periods of Modular Forms / Kartik Prasanna 251

Functoriality and Special Values of L-Functions / A. Raghuram, Freydoon Shahidi 271

Bounds for Matrix Coefficients and Arithmetic Applications / Ramin Takloo-Bighash 295.

ISBN:

9780817644963

0817644962

OCLC:

86167941