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

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 c...

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Bibliographic Details
Published inScience China. Mathematics Vol. 66; no. 12; pp. 2731 - 2748
Main Authors Goldfeld, Dorian, Stade, Eric, Woodbury, Michael
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 01.12.2023
Springer Nature B.V
Subjects
Affine transformations
Applications of Mathematics
Functional equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Whittaker functions
11F72
Langlands Eisenstein series
general linear group
functional equations
automorphic forms
11F55
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Summary: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.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-023-2213-y