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A zero density estimate and fractional imaginary parts of zeros for
$\textrm{GL}_2$ L-functions
Published online by Cambridge University Press: 28 December 2022
Abstract
We prove an analogue of Selberg’s zero density estimate for
$\zeta(s)$
that holds for any
$\textrm{GL}_2$
L-function. We use this estimate to study the distribution of the vector of fractional parts of
$\gamma\boldsymbol{\alpha}$
, where
$\boldsymbol{\alpha}\in\mathbb{R}^n$
is fixed and
$\gamma$
varies over the imaginary parts of the nontrivial zeros of a
$\textrm{GL}_2$
L-function.
MSC classification
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 174 , Issue 3 , May 2023 , pp. 605 - 630
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on behalf of Cambridge Philosophical Society
References
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