The fourth power mean of Dirichlet L-functions in Fq [T]
dc.contributor.author | Bueno De Andrade, JC | |
dc.contributor.author | Yiasemides, M | |
dc.date.accessioned | 2020-01-28T12:15:39Z | |
dc.date.issued | 2020-02-13 | |
dc.description.abstract | We prove results on moments of L-functions in the function field setting, where the moment averages are taken over primitive characters of modulus R, where R is a polynomial in Fq[T]. We consider the behaviour as deg R → ∞ and the cardinality of the finite field is fixed. Specifically, we obtain an exact formula for the second moment provided that R is square-full, an asymptotic formula for the second moment for any R, and an asymptotic formula for the fourth moment for any R. The fourth moment result is a function field analogue of Soundararajan’s result in the number field setting that improved upon a previous result by Heath-Brown. Both the second and fourth moment results extend work done by Tamam in the function field setting who focused on the case where R is prime. As a prerequisite for the fourth moment result, we obtain, for the special case of the divisor function, the function field analogue of Shiu’s generalised Brun-Titchmarsh theorem. | en_GB |
dc.description.sponsorship | Leverhulme Trust | en_GB |
dc.description.sponsorship | Engineering and Physical Sciences Research Council (EPSRC) | en_GB |
dc.identifier.citation | Published online 13 February 2020 | en_GB |
dc.identifier.doi | 10.1007/s13163-020-00350-2 | |
dc.identifier.grantnumber | RPG-2017-320 | en_GB |
dc.identifier.uri | http://hdl.handle.net/10871/40609 | |
dc.language.iso | en | en_GB |
dc.publisher | Springer Verlag | en_GB |
dc.rights | © The Author(s) 2020. 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 | moments of L-functions | en_GB |
dc.subject | Dirichlet characters | en_GB |
dc.subject | polynomials | en_GB |
dc.subject | function fields | en_GB |
dc.title | The fourth power mean of Dirichlet L-functions in Fq [T] | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2020-01-28T12:15:39Z | |
dc.identifier.issn | 1139-1138 | |
dc.description | This is the final version. Available on open access from Springer Verlag via the DOI in this record | en_GB |
dc.identifier.journal | Revista Matemática Complutense | en_GB |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_GB |
dcterms.dateAccepted | 2020-01-24 | |
exeter.funder | ::Leverhulme Trust | en_GB |
rioxxterms.version | VoR | en_GB |
rioxxterms.licenseref.startdate | 2020-01-24 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2020-01-28T11:54:00Z | |
refterms.versionFCD | AM | |
refterms.dateFOA | 2020-02-27T13:54:20Z | |
refterms.panel | B | en_GB |
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Except where otherwise noted, this item's licence is described as © The Author(s) 2020. 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/