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Journal of the Ramanujan Mathematical Society

Volume 37, Issue 1, March 2022  pp. 31–47.

A note on simultaneous nonvanishing of Dirichlet L-functions and twists of Hecke-Maass L-functions

Authors:  Qingfeng Sun
Author institution:School of Mathematics and Statistics, Shandong University, Weihai, Weihai Shandong 264209, China

Summary:  We prove that given a Hecke-Maass cusp form f for SL{2}(Z) and a sufficiently large integer q = q{1}q{2} with q{j} = √q being prime numbers for j = 1, 2, there exists a primitive Dirichlet character χ of conductor q such that L(1/2, f ⊗ χ)L(1/2, χ) ≠ 0. To prove this, we establish asymptotic formulas of L(1/2, f ⊗ χ)L(1/2, χ) over the family of even primitive Dirichlet characters χ of conductor q for more general q.

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