Periods of automorphic forms

Jacquet, Hervé; Lapid, Erez; Rogawski, Jonathan

doi:10.1090/S0894-0347-99-00279-9

Periods of automorphic forms
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by Hervé Jacquet, Erez Lapid and Jonathan Rogawski

J. Amer. Math. Soc. 12 (1999), 173-240

DOI: https://doi.org/10.1090/S0894-0347-99-00279-9

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Abstract:

Let $E/F$ be a quadratic extension of number fields and $G= \operatorname {Res}_{E/F}H$, where $H$ is a reductive group over $F$. We define the integral (in general, non-convergent) of an automorphic form on $G$ over $H(F)\backslash H(\mathbb A)^1$ via regularization. This regularized integral is used to derive a formula for the integral over $H(F)\backslash H(\mathbb A)^1$ of a truncated Eisenstein series on $G$. More explicit results are obtained in the case $H=GL(n)$. These results will find applications in the expansion of the spectral side of the relative trace formula.

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