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Low-lying zeros of quadratic Dirichlet L-functions: lower order terms for extended support
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). Univ Lethbridge, Canada.
2017 (English)In: Compositio Mathematica, ISSN 0010-437X, E-ISSN 1570-5846, Vol. 153, no 6, 1196-1216 p.Article in journal (Refereed) Published
Abstract [en]

We study the 1-level density of low-lying zeros of Dirichlet L-functions attached to real primitive characters of conductor at most X. Under the generalized Riemann hypothesis, we give an asymptotic expansion of this quantity in descending powers of log X, which is valid when the support of the Fourier transform of the corresponding even test function phi is contained in (-2, 2). We uncover a phase transition when the supremum sigma of the support of (phi) over cap reaches 1, both in the main term and in the lower order terms. A new lower order term appearing at sigma = 1 involves the quantity (phi) over cap (1), and is analogous to a lower order term which was isolated by Rudnick in the function field case.

Place, publisher, year, edition, pages
Cambridge University Press, 2017. Vol. 153, no 6, 1196-1216 p.
Keyword [en]
zeros of L-functions, Katz-Sarnak heuristics, quadratic Dirichlet L-functions, 1-level density
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-211030DOI: 10.1112/S0010437X17007059ISI: 000403416600003OAI: oai:DiVA.org:kth-211030DiVA: diva2:1121666
Funder
EU, FP7, Seventh Framework Programme, DFF-1325-00058
Note

QC 20170712

Available from: 2017-07-12 Created: 2017-07-12 Last updated: 2017-07-12Bibliographically approved

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