Eisenstein Series and Applications

Ben Brubaker, Daniel Bump, Solomon Friedberg (auth.), Wee Teck Gan, Stephen S. Kudla, Yuri Tschinkel (eds.)0817644962, 9780817646394, 9780817644963

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?

Contributors include: B. Brubaker, D. Bump, J. Franke, S. Friedberg, W.T. Gan, P. Garrett, M. Harris, D. Jiang, S.S. Kudla, E. Lapid, K. Prasanna, A. Raghuram, F. Shahidi, R. Takloo-Bighash

Table of contents :
Front Matter….Pages i-x
Twisted Weyl Group Multiple Dirichlet Series: The Stable Case….Pages 1-26
A Topological Model for Some Summand of the Eisenstein Cohomology of Congruence Subgroups….Pages 27-85
The Saito-Kurokawa Space of PGS p4 and Its Transfer to Inner Forms….Pages 87-123
Values of Archimedean Zeta Integrals for Unitary Groups….Pages 125-148
A Simple Proof of Rationality of Siegel-Weil Eisenstein Series….Pages 149-185
Residues of Eisenstein Series and Related Problems….Pages 187-204
Some Extensions of the Siegel-Weil Formula….Pages 205-237
A Remark on Eisenstein Series….Pages 239-249
Arithmetic Aspects of the Theta Correspondence and Periods of Modular Forms….Pages 251-269
Functoriality and Special Values of L -Functions….Pages 271-293
Bounds for Matrix Coefficients and Arithmetic Applications….Pages 295-314