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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