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?
Mục lục
Twisted Weyl Group Multiple Dirichlet Series: The Stable Case.- A Topological Model for Some Summand of the Eisenstein Cohomology of Congruence Subgroups.- The Saito-Kurokawa Space of PGSp4 and Its Transfer to Inner Forms.- Values of Archimedean Zeta Integrals for Unitary Groups.- A Simple Proof of Rationality of Siegel-Weil Eisenstein Series.- Residues of Eisenstein Series and Related Problems.- Some Extensions of the Siegel-Weil Formula.- A Remark on Eisenstein Series.- Arithmetic Aspects of the Theta Correspondence and Periods of Modular Forms.- Functoriality and Special Values of L-Functions.- Bounds for Matrix Coefficients and Arithmetic Applications.
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