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Media type:
E-Article
Title:
Periods of automorphic forms
Contributor:
Jacquet, Hervé;
Lapid, Erez;
Rogawski, Jonathan
Published:
American Mathematical Society (AMS), 1999
Published in:
Journal of the American Mathematical Society, 12 (1999) 1, Seite 173-240
Language:
English
DOI:
10.1090/s0894-0347-99-00279-9
ISSN:
0894-0347;
1088-6834
Origination:
Footnote:
Description:
Let E / F E/F be a quadratic extension of number fields and G = Res E / F H G= \operatorname {Res}_{E/F}H , where H H is a reductive group over F F . We define the integral (in general, non-convergent) of an automorphic form on G G over H ( F ) ∖ H ( A ) 1 H(F)\backslash H(\mathbb A)^1 via regularization. This regularized integral is used to derive a formula for the integral over H ( F ) ∖ H ( A ) 1 H(F)\backslash H(\mathbb A)^1 of a truncated Eisenstein series on G G . More explicit results are obtained in the case H = G L ( n ) H=GL(n) . These results will find applications in the expansion of the spectral side of the relative trace formula.