The functional equations of Langlands Eisenstein series for SL(n,Z)  

作　　者：Dorian Goldfeld Eric Stade Michael Woodbury 

机构地区：[1]Department of Mathematics,Columbia University,New York,NY 10027,USA [2]Department of Mathematics,University of Colorado Boulder,Boulder,Colorado 80309,USA [3]Department of Mathematics,Rutgers,The State University of New Jersey,Piscataway,NJ 08854-8019,USA

出　　处：《Science China Mathematics》2023年第12期2731-2748,共18页中国科学：数学（英文版）

基　　金：supported by Simons Collaboration(Grant No.567168)。

摘　　要：In this paper,we present a very simple explicit description of Langlands Eisenstein series for SL(n,Z).The functional equations of these Eisenstein series are heuristically derived from the functional equations of certain divisor sums and certain Whittaker functions that appear in the Fourier coefficients of the Eisenstein series.We conjecture that the functional equations are unique up to a real affine transformation of the s variables defining the Eisenstein series and prove the uniqueness conjecture in certain cases.

关 键 词：Langlands Eisenstein series functional equations automorphic forms general linear group 

分 类 号：O156[理学—数学]