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15 May 2019 Weak subconvexity without a Ramanujan hypothesis
Kannan Soundararajan, Jesse Thorner
Duke Math. J. 168(7): 1231-1268 (15 May 2019). DOI: 10.1215/00127094-2018-0065

Abstract

We describe a new method to obtain weak subconvexity bounds for L-functions with mild hypotheses on the size of the Dirichlet coefficients. We verify these hypotheses for all automorphic L-functions and (with mild restrictions) the Rankin–Selberg L-functions attached to two automorphic representations. The proof relies on a new unconditional log-free zero density estimate for Rankin–Selberg L-functions.

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Kannan Soundararajan. Jesse Thorner. "Weak subconvexity without a Ramanujan hypothesis." Duke Math. J. 168 (7) 1231 - 1268, 15 May 2019. https://doi.org/10.1215/00127094-2018-0065

Information

Received: 10 April 2018; Revised: 29 October 2018; Published: 15 May 2019
First available in Project Euclid: 3 May 2019

zbMATH: 07078883
MathSciNet: MR3953433
Digital Object Identifier: 10.1215/00127094-2018-0065

Subjects:
Primary: 11F67
Secondary: 11F66, 11M41

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 7 • 15 May 2019
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