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Zeros of GL2 𝐿-functions on the critical line

  • Nickolas Andersen and Jesse Thorner EMAIL logo
From the journal Forum Mathematicum

Abstract

We use Levinson’s method and the work of Blomer and Harcos on the GL2 shifted convolution problem to prove that at least 6.96 % of the nontrivial zeros of the 𝐿-function of a GL2 automorphic form lie on the critical line.

MSC 2010: 11F66

Award Identifier / Grant number: DMS-1701638

Funding statement: This work began while the first author was funded by NSF grant DMS-1701638 and the second author was a postdoctoral researcher at Stanford University (funded by a NSF Mathematical Sciences Postdoctoral Fellowship).

Acknowledgements

All computations were performed using Mathematica 12. We thank the anonymous referee for the helpful comments.

  1. Communicated by: Valentin Blomer

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Received: 2020-04-29
Revised: 2020-12-21
Published Online: 2021-02-02
Published in Print: 2021-03-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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