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arXiv · 1308.2253

Periods and nonvanishing of central L-values for GL(2n)

Brooke Feigon·Kimball Martin·David Whitehouse
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Abstract

Let $\pi$ be a cuspidal automorphic representation of PGL($2n$) over a number field $F$, and $\eta$ the quadratic idele class character attached to a quadratic extension $E/F$. Guo and Jacquet conjectured a relation between the nonvanishing of $L(1/2,\pi)L(1/2, \pi \otimes \eta)$ for $\pi$ of symplectic type and the nonvanishing of certain GL($n,E$) periods. When $n=1$, this specializes to a well-known result of Waldspurger. We prove this conjecture, and related global results, under some local hypotheses using a simple relative trace formula. We then apply these global results to obtain local results on distinguished supercuspidal representations, which partially establish a conjecture of Prasad and Takloo-Bighash.

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Brooke Feigon, Kimball Martin, David Whitehouse. 2013-08-09. Periods and nonvanishing of central L-values for GL(2n). https://doi.org/10.1007/s11856-018-1657-5

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