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arXiv · 1411.4545

Simultaneous nonvanishing of Dirichlet $L$-functions and twists of Hecke-Maass L-functions

Soumya Das·Rizwanur Khan
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Abstract

We prove that given a Hecke-Maass form $f$ for $\text{SL}(2, \mathbb{Z})$ and a sufficiently large prime $q$, there exists a primitive Dirichlet character $\chi$ of conductor $q$ such that the $L$-values $L(\tfrac{1}{2}, f \otimes \chi)$ and $L(\tfrac{1}{2}, \chi)$ do not vanish. We expect the same method to work for any large integer $q$.

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Soumya Das, Rizwanur Khan. 2014-11-17. Simultaneous nonvanishing of Dirichlet $L$-functions and twists of Hecke-Maass L-functions. https://arxiv.org/abs/1411.4545

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