03929nam 22005775i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001600172072001600188072002300204082001400227245012300241264004600364300003200410336002600442337002600468338003600494347002400530490003500554505067900589520140001268650001702668650002402685650002402709650001602733650002502749650002902774650001402803650001902817650001702836650001902853650003302872650001402905650002402919650003602943700002802979700003103007700003003038710003403068773002003102776003603122830003503158856004803193912001403241999001903255952007703274978-0-8176-4639-4DE-He21320180115171437.0cr nn 008mamaa100301s2008 xxu| s |||| 0|eng d a97808176463949978-0-8176-4639-47 a10.1007/978-0-8176-4639-42doi 4aQA241-247.5 7aPBH2bicssc 7aMAT0220002bisacsh04a512.722310aEisenstein Series and Applicationsh[electronic resource] /cedited by Wee Teck Gan, Stephen S. Kudla, Yuri Tschinkel. 1aBoston, MA :bBirkhèauser Boston,c2008. aX, 314 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aProgress in Mathematics ;v2580 aTwisted 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. aEisenstein 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. 0aMathematics. 0aAlgebraic geometry. 0aTopological groups. 0aLie groups. 0aApplied mathematics. 0aEngineering mathematics. 0aGeometry. 0aNumber theory.14aMathematics.24aNumber Theory.24aApplications of Mathematics.24aGeometry.24aAlgebraic Geometry.24aTopological Groups, Lie Groups.1 aGan, Wee Teck.eeditor.1 aKudla, Stephen S.eeditor.1 aTschinkel, Yuri.eeditor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780817644963 0aProgress in Mathematics ;v25840uhttp://dx.doi.org/10.1007/978-0-8176-4639-4 aZDB-2-SMA c369959d369959 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK