New York Journal of Mathematics
Volume 20 (2014) 153-181


João Pedro Boavida

Compact periods of Eisenstein series of orthogonal groups of rank one at even primes

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Published: February 10, 2014
Keywords: Eisenstein series, period, automorphic, L-function, orthogonal group
Subject: Primary 11F67; Secondary 11E08, 11E95, 11S40

Fix a number field k with its adele ring A. Let G=O(n+3) be an orthogonal group of k-rank 1 and H=O(n+2) a k-anisotropic subgroup. We have previously described how to factor the global period
(Eφ,F)H = ∫Hk\HAEφ⋅\bar{F}
of a spherical Eisenstein series Eφ of G against a cuspform F of H into an Euler product. Here, we describe how to evaluate the factors at even primes. When the local field is unramified, we carry out the computation in all cases. We show also concrete examples of the complete period when k = Q. The results are consistent with the Gross-Prasad conjecture.

Author information

Departamento de Matemática, Instituto Superior Técnico,Universidade de Lisboa, Av. Prof. Dr. Cavaco Silva,2744-016 Porto Salvo, Portugal