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arXiv · 0705.1576

On Shalika Periods and a Theorem of Jacquet-Martin

Wee Teck Gan·Shuichiro Takeda
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Abstract

Let πbe a cuspidal automorphic representation of GL_4 with central character μ^2. It is known that πhas Shalika period with respect to μif and only if the L-function L^S(s, π, \bigwedge^2\otimesμ^{-1}) has a pole at s=1. Recentlt, Jacquet and Martin considered the analogous question for cuspidal representations π_D of the inner form GL_2(D)(\A), and obtained a partial result via the relative trace formula. In this paper, we provide a complete solution to this problem via the method of theta correspondence, and give necessary and sufficient conditions for the existence of Shalika period for π_D. We also resolve the analogous question in the local setting.

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Wee Teck Gan, Shuichiro Takeda. 2008-05-18. On Shalika Periods and a Theorem of Jacquet-Martin. https://arxiv.org/abs/0705.1576

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