Selberg's normal density theorem for automorphic \(L\)-functions for \(\mathrm{GL}_m\)
type: Item
instance of: scholarly article
title: Selberg's normal density theorem for automorphic \(L\)-functions for \(\mathrm{GL}_m\)
zbMATH Open document ID: 1153.11024
author: Yan Qu
publication date: 2008-01-04T00:00:00Z
review text: Let \(\pi\) be a cuspidal (irreducible, unitary) representation of \(\text{GL}(m,\mathbb A_{\mathbb Q})\), \(m\geq 2\). Let \(L(s,\pi)\) be the \(L\)-function of \(\pi\). Generalizing Selberg's result for the Riemann zeta-function, assuming the Generalized Riemann Hypothesis for \(L(s,\pi)\), the paper estimates the normal density of primes in short intervals for the automorphic \(L\)-function \(L(s,\pi)\), using analytic techniques. see also the author's previous paper [J. Number Theory 122, no. 1, 84--99 (2007; Zbl 1153.11023)]
reviewed by: Yuval Z. Flicker
Mathematics Subject Classification ID: 11F66
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11M41
zbMATH DE Number: 5223497
zbMATH Keywords: Automorphic \(L\)-function
zbMATH Keywords: Selberg's normal density theorem
MaRDI profile type: Publication
full work available at URL: s10114-005-0926-5
OpenAlex ID: W2125722456
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DOI: 10.1007/S10114-005-0926-5
published in: Acta Mathematica Sinica, English Series
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description: scientific article