Titlebook: Eisenstein Series and Applications; Wee Teck Gan,Stephen S. Kudla,Yuri Tschinkel Book 2008 Birkh?user Boston 2008 Area.Congruence.Matrix.V

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溫順

Some Extensions of the Siegel-Weil Formula,We survey recent extensions of the classical Siegel-Weil formula linking special values of certain Eisenstein series with integrals of theta functions to relations between residues of Eisenstein series and regularized integrals of theta functions.

Mendicant

A Remark on Eisenstein Series,We prove meromorphic continuation of Eisenstein series for smooth but not necessarily .-finite sections.

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Misnomer

Functoriality and Special Values of ,-Functions,This is a semi-expository article concerning Langlands functoriality and Deligne’s conjecture on the special values of .-functions. The emphasis is on symmetric power .-functions associated to a holomorphic cusp form, while appealing to a recent work of Mahnkopf on the special values of automorphic .-functions.

鳴叫

Bounds for Matrix Coefficients and Arithmetic Applications,We explain an important result of Hee Oh [20] on bounding matrix coefficients of semi-simple groups and survey some applications.

Amylase

https://doi.org/10.1007/978-3-531-92202-7in [2]. Brubaker, Bump, and Friedberg [4] provided for when n is sufficiently large; the coefficients involve .-th order Gauss sums and reflect the combinatorics of the root system. Conjecturally, these functions coincide with Whittaker coefficients of metaplectic Eisenstein series, but they are stu

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同音

https://doi.org/10.1007/978-3-531-91129-8 By contrast, the traditional approach is to determine the residues of Eisenstein series in terms of certain .-functions attached to the cuspidal data. The relation between these two methods is the general conjecture which relates periods on the cuspidal data to the existence of poles or the special

phlegm

Wee Teck Gan,Stephen S. Kudla,Yuri TschinkelBrings 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