Periods of Eisenstein series: the Galois case
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 \textit{H. Jacquet, E. Lapid} and \textit{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.
scientific article; zbMATH DE number 2034299
scientific article