Wee Teck Gan, A. Raghuram
Published 2012-07-19, updated 2012-11-25Version 2
A cuspidal automorphic representation \pi of a group G is said to to be distinguished with respect to a subgroup H if the integral of f along H is nonzero for a cusp form f in the space of \pi. Such period integrals are related to (non)vanishing of interesting L-values and also to Langlands functoriality. This article discusses a general principle, labelled arithmeticity, which roughly states that "\pi is H-distinguished if and only if any Galois conjugate of \pi is H-distinguished." We study this principle via several examples; starting with GL(2) and leading up to more complicated situations where the ambient group is a higher GL(n) or a classical group.
Comments: 32 pages. The final version is to appear in the proceedings of the International Colloquium on Automorphic Representations and L-functions, held in TIFR, Mumbai, January 2012
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Special values of adjoint L-functions and congruences for automorphic forms on GL(n) over a number field
Eulerianity of Fourier coefficients of automorphic forms
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