The integral moments and ratios of quadratic Dirichlet L-functions over monic irreducible polynomials in Fq[T]
dc.contributor.author | Andrade, JC | |
dc.contributor.author | Jung, H | |
dc.contributor.author | Shamesaldeen, A | |
dc.date.accessioned | 2021-04-19T14:29:26Z | |
dc.date.issued | 2021-05-05 | |
dc.description.abstract | In this paper, we extend to the function field setting the heuristics formerly developed by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments of L-functions. We also adapt to the function field setting the heuristics first developed by Conrey, Farmer and Zirnbauer to the study of mean values of ratios of L-functions. Specifically, the focus of this paper is on the family of quadratic Dirichlet L-functions L(s, χP ) where the character χ is defined by the Legendre symbol for polynomials in Fq[T] with Fq a finite field of odd cardinality and the averages are taken over all monic and irreducible polynomials P of a given odd degree. As an application, we also compute the formula for the one-level density for the zeros of these L-functions. | en_GB |
dc.description.sponsorship | Leverhulme Trust | en_GB |
dc.description.sponsorship | National Research Foundation of Korea | |
dc.description.sponsorship | Government of Kuwait | |
dc.identifier.citation | Published online 5 May 2021 | en_GB |
dc.identifier.doi | 10.1007/s11139-021-00422-x | |
dc.identifier.grantnumber | RPG-2017-320 | en_GB |
dc.identifier.grantnumber | 2020R1F1A1A01066105 | |
dc.identifier.uri | http://hdl.handle.net/10871/125392 | |
dc.language.iso | en | en_GB |
dc.publisher | Springer | en_GB |
dc.rights | © The Author(s) 2021. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ | |
dc.subject | function fields | en_GB |
dc.subject | integral moments of L–functions | en_GB |
dc.subject | quadratic Dirichlet L–functions | en_GB |
dc.subject | ratios conjecture | en_GB |
dc.title | The integral moments and ratios of quadratic Dirichlet L-functions over monic irreducible polynomials in Fq[T] | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2021-04-19T14:29:26Z | |
dc.identifier.issn | 1382-4090 | |
dc.description | This is the final version. Available on open access from Springer via the DOI in this record. | en_GB |
dc.identifier.journal | Ramanujan Journal | en_GB |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_GB |
dcterms.dateAccepted | 2021-03-01 | |
exeter.funder | ::Leverhulme Trust | en_GB |
rioxxterms.funder | Leverhulme Trust | en_GB |
rioxxterms.identifier.project | RPG-2017-320 | en_GB |
rioxxterms.version | VoR | en_GB |
rioxxterms.licenseref.startdate | 2021-03-01 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2021-03-01T10:12:37Z | |
refterms.versionFCD | AM | |
refterms.dateFOA | 2021-05-14T14:54:36Z | |
refterms.panel | B | en_GB |
rioxxterms.funder.project | 0f55c787-be27-419f-abe2-cf88fb0d8d83 | en_GB |
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Except where otherwise noted, this item's licence is described as © The Author(s) 2021. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/