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arXiv · 1207.4641

Arithmeticity for periods of automorphic forms

Wee Teck Gan·A. Raghuram
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Abstract

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.

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Wee Teck Gan, A. Raghuram. 2012-07-19. Arithmeticity for periods of automorphic forms. https://arxiv.org/abs/1207.4641

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