Eisenstein Series and Applications

ISBN-13: 9780817644963 / Angielski / Twarda / 2008 / 314 str.

Wee Teck Gan;Stephen S. Kudla;Yuri Tschinkel

Opis

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? 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

Spis treści

Preface.-Twisted Weyl Group Multiple Dirichlet Series: The Stable Case by Ben Brubaker, Daniel Bump, Solomon Friedberg.-A Topological Model for some Summand of the Eisenstein Cohomology of Congruence Subgroups by Jens Franke.-The Saito-Lurokawa Space of PGSp4 and its Transfer to Inner Forms by Wee Teck Gan.-Values of Archimedean Zeta Integrals for Unitary Groups by Paul Garrett.-A Simple Proof of Rationality of Siegel-Weil Eisenstein Series by Michael Harris.-Residues of Eisenstein Series and Related Problems by Dihua Jiang.-Some Extensions of the Siegel-Weil Formula by Stephen S. Kudla.-A Remark on Eisenstein Series by Erez M. Lapid.-Arithmetic Aspects of the Theta Correspondence and Periods of Modular Forms by Kartik Prasanna.-Functoriality and Special Values of L-functions by A. Raghuram, Freydoon Shahidi.-Bounds for Matrix Coefficients and Arithmetic Applications by Ramin Takloo-Bighash.

Blurb

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