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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Simultaneous nonvanishing of $GL(2) \times GL(2)$ and $GL(2)$ $L$-functions
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Proc. Amer. Math. Soc. 142 (2014), 1953-1964 Request permission

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
  • Received by editor(s): July 11, 2012
  • Published electronically: March 7, 2014
  • Communicated by: Ken Ono
  • © Copyright 2014 American Mathematical Society
  • 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
  • MathSciNet review: 3182014