Manuscripta Mathematica

, Volume 134, Issue 3, pp 309–342

Simultaneous nonvanishing of automorphic L-functions at the central point


DOI: 10.1007/s00229-010-0396-7

Cite this article as:
Xu, Z. manuscripta math. (2011) 134: 309. doi:10.1007/s00229-010-0396-7


Let g be a holomorphic Hecke eigenform and {uj} an orthonormal basis of even Hecke–Maass forms for \({\textup{SL}(2,\mathbb{Z})}\). Denote L(s, g × uj) and L(s, uj) 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 uj’s such that \({L(\frac{1}{2},g\times u_j)L(\frac{1}{2},u_j)\neq0}\).

Mathematics Subject Classification (2000)

11M41 11S40 

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJinanPeople’s Republic of China

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