Article

Manuscripta Mathematica

, Volume 134, Issue 3, pp 309-342

Simultaneous nonvanishing of automorphic L-functions at the central point

  • Zhao XuAffiliated withSchool of Mathematics, Shandong University Email author 

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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 \({L(\frac{1}{2},g\times u_j)L(\frac{1}{2},u_j)\neq0}\).

Mathematics Subject Classification (2000)

11M41 11S40