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Simultaneous nonvanishing of automorphic L-functions at the central point

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Abstract

Let g be a holomorphic Hecke eigenform and {u j } an orthonormal basis of even Hecke–Maass forms for \({\textup{SL}(2,\mathbb{Z})}\). Denote L(s, g × u j ) and L(s, u j ) the corresponding L-functions. In this paper, we give an asymptotic formula for the average of \({L(\frac{1}{2},g\times u_j)L(\frac{1}{2},u_j)}\), from which we derive that there are infinitely many u j ’s such that \({L(\frac{1}{2},g\times u_j)L(\frac{1}{2},u_j)\neq0}\).

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  1. School of Mathematics, Shandong University, Jinan, 250100, People’s Republic of China

    Zhao Xu

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Xu, Z. Simultaneous nonvanishing of automorphic L-functions at the central point. manuscripta math. 134, 309–342 (2011). https://doi.org/10.1007/s00229-010-0396-7

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  • DOI: https://doi.org/10.1007/s00229-010-0396-7

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