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A log-free zero-density estimate and small gaps in coefficients of L-functions

Akbary, Amir; Trudgian, Timothy S


Let L(s,π×π ′ ) be the Rankin--Selberg L -function attached to automorphic representations π and π ′ . Let π ~ and π ~ ′ denote the contragredient representations associated to π and π ′ . Under the assumption of certain upper bounds for coefficients of the logarithmic derivatives of L(s,π×π ~ ) and L(s,π ′ ×π ~ ′ ) , we prove a log-free zero-density estimate for L(s,π×π ′ ) which generalises a result due to Fogels in the context of Dirichlet L -functions. We then employ this...[Show more]

CollectionsANU Research Publications
Date published: 2014-04-14
Type: Journal article
Source: To appear in International Mathematics Research Notices
DOI: 10.1093/imrn/rnu065


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