Author:
BECKWITH OLIVIA,LIU DI,THORNER JESSE,ZAHARESCU ALEXANDRU
Abstract
AbstractWe 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.
Publisher
Cambridge University Press (CUP)
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