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2017 Test vectors and central $L$-values for ${\rm GL}(2)$
Daniel File, Kimball Martin, Ameya Pitale
Algebra Number Theory 11(2): 253-318 (2017). DOI: 10.2140/ant.2017.11.253

Abstract

We determine local test vectors for Waldspurger functionals for GL2, in the case where both the representation of GL2 and the character of the degree two extension are ramified, with certain restrictions. We use this to obtain an explicit version of Waldspurger’s formula relating twisted central L-values of automorphic representations on GL2 with certain toric period integrals. As a consequence, we generalize an average value formula of Feigon and Whitehouse, and obtain some nonvanishing results.

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Daniel File. Kimball Martin. Ameya Pitale. "Test vectors and central $L$-values for ${\rm GL}(2)$." Algebra Number Theory 11 (2) 253 - 318, 2017. https://doi.org/10.2140/ant.2017.11.253

Information

Received: 19 May 2014; Revised: 22 September 2016; Accepted: 26 September 2016; Published: 2017
First available in Project Euclid: 16 November 2017

MathSciNet: MR3641876
zbMATH: 06722471
Digital Object Identifier: 10.2140/ant.2017.11.253

Subjects:
Primary: 11F67
Secondary: 11F41, 11F66, 11F70

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 2 • 2017
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