A case of simultaneous non-vanishing of automorphic $L$-functions
Volume 182 / 2018
Acta Arithmetica 182 (2018), 1-11
MSC: Primary 11F67; Secondary 11F11, 11F66.
DOI: 10.4064/aa8179-9-2017
Published online: 18 December 2017
Abstract
We show that for $k\geq 12$ even, there exists an effectively computable constant $q_k$ such that for any prime $q \gt q_k$, there exists a newform $f$ of weight $k$ and level $q$ such that $$ L(1/2,f)L(1/2,\mathop{\rm Sym}\nolimits^2 f)\neq 0. $$
