Simultaneous nonvanishing of $GL(2) \times GL(2)$ and $GL(2)$ $L$-functions
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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 $L \left (\tfrac {1}{2}, g \right ) L\left (\tfrac {1}{2}, f \times g \right ) \ne 0.$References
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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