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LOW-LYING ZEROS OF QUADRATIC DIRICHLET L-FUNCTIONS: A TRANSITION IN THE RATIOS CONJECTURE
Univ Ottawa, Dept Math & Stat, 585 King Edward, Ottawa, ON K1N 6N5, Canada..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Chalmers Univ Technol, Dept Math Sci, SE-41296 Gothenburg, Sweden.;Univ Gothenburg, SE-41296 Gothenburg, Sweden..
2018 (English)In: Quarterly Journal of Mathematics, ISSN 0033-5606, E-ISSN 1464-3847, Vol. 69, no 4, p. 1129-1149Article in journal (Refereed) Published
Abstract [en]

We study the 1-level density of low-lying zeros of quadratic Dirichlet L-functions by applying the L-functions Ratios Conjecture. We observe a transition in the main term as was predicted by the Katz-Sarnak heuristic as well as in the lower-order terms when the support of the Fourier transform of the corresponding test function reaches the point 1. Our results are consistent with those obtained in previous work under GRH and are furthermore analogous to results of Rudnick in the function field case.

Place, publisher, year, edition, pages
OXFORD UNIV PRESS , 2018. Vol. 69, no 4, p. 1129-1149
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Mathematics
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URN: urn:nbn:se:kth:diva-243969DOI: 10.1093/qmath/hay018ISI: 000456696100002OAI: oai:DiVA.org:kth-243969DiVA, id: diva2:1293002
Note

QC 20190301

Available from: 2019-03-01 Created: 2019-03-01 Last updated: 2019-03-01Bibliographically approved

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