Periods of Eisenstein series: the Galois case. (English) Zbl 1037.11033

Lapid, Erez M.; Rogawski, Jonathan D.

Duke Math. J. 120, No. 1, 153-226 (2003).

In this paper the periods of Eisenstein series are studied in the following case. Let \(H\) be a connected reductive group over a number field \(F\) and let \(G = \text{Res}_{E/F}\,H\), where \(E/F\) is a quadratic extension. The period of an automorphic form on \(G\) with respect to \(H\) is defined as a regularized integral. The main result of the paper is an expression for the period of a cuspidal Eisenstein series as a sum of intertwining periods (the name of these functionals is explained in H. Jacquet, E. Lapid and J. Rogawski [J. Am. Math. Soc. 12, 173–240 (1999; Zbl 1012.11044)] ). That sum of intertwining periods has a meromorphic continuation and satisfies a set of functional equations. From the main result one also deduces a relative analogue of the Maass-Selberg relations.

Reviewer: J. G. M. Mars (Utrecht)

MSC:

11F67	Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11F72	Spectral theory; trace formulas (e.g., that of Selberg)

Keywords:

connected reductive group; cuspidal Eisenstein series; sum of intertwining periods; Maass-Selberg relations

Citations:

Zbl 1012.11044

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