Simultaneous non-vanishing of $GL(3)\times GL(2)$ and GL(2) $L$-functions

Rizwanur Khan

doi:10.1017/S0305004111000806

Simultaneous non-vanishing of $GL(3)\times GL(2)$ and GL(2) $L$-functions

Number Theory 2015-05-27 v2

Authors: Rizwanur Khan

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Abstract

Fix $g$ a Hecke-Maass form for $SL_3(\mathbb{Z})$ . Let $q$ be any large prime number. In the family of holomorphic newforms $f$ of level $q$ and fixed weight, we find the average value of the product $L(\half,g\times f)L(\half,f)$ . From this we derive a result on the simultaneous non-vanishing of these $L$ -functions at the central point.

Keywords

L-functions Hecke-Maass form holomorphic newform simultaneous non-vanishing automorphic forms

Cite

@article{arxiv.1103.5937,
  title  = {Simultaneous non-vanishing of $GL(3)\times GL(2)$ and GL(2) $L$-functions},
  author = {Rizwanur Khan},
  journal= {arXiv preprint arXiv:1103.5937},
  year   = {2015}
}

Comments

19 pages

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