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Simultaneous nonvanishing of $ GL(2) \times GL(2)$ and $ GL(2)$ $ L$-functions


Author: Sheng-Chi Liu
Journal: Proc. Amer. Math. Soc. 142 (2014), 1953-1964
MSC (2010): Primary 11F11, 11M99
DOI: https://doi.org/10.1090/S0002-9939-2014-12066-1
Published electronically: March 7, 2014
MathSciNet review: 3182014
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ f$ be a fixed holomorphic Hecke cusp form for $ SL(2, \mathbb{Z})$. We prove that for each $ K$ large enough, there exists a holomorphic Hecke cusp form $ g$ of weight $ k$ with $ K \le k \le 2K$ such that $ L \left (\tfrac {1}{2}, g \right ) L\left (\tfrac {1}{2}, f \times g \right ) \ne 0.$


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Additional Information

Sheng-Chi Liu
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Address at time of publication: Department of Mathematics, Washington State University, Pullman, Washington 99164-3113
Email: scliu@math.wsu.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12066-1
Received by editor(s): July 11, 2012
Published electronically: March 7, 2014
Communicated by: Ken Ono
Article copyright: © Copyright 2014 American Mathematical Society

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