Publication:
On the mean square average of special values of L-functions

dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorAlkan, Emre
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T22:58:04Z
dc.date.issued2011
dc.description.abstractLet chi be a Dirichlet character and L(s, chi) be its L-function. Using weighted averages of Gauss and Ramanujan sums, we find exact formulas involving Jordan's and Euler's totient function for the mean square average of L(1, chi) when chi ranges over all odd characters modulo k and L(2, chi) when x ranges over all even characters modulo k. In principle, using our method, it is always possible to find the mean square average of L(r, chi) if chi and r >= 1 have the same parity and chi ranges over all odd (or even) characters modulo k, though the required calculations become formidable when r >= 3. Consequently, we see that for almost all odd characters modulo k, vertical bar L(1, chi)vertical bar < phi(k), where phi(x) is any function monotonically tending to infinity. (C) 2011 Elsevier Inc. All rights reserved.
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue8
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.sponsorshipTuba-Gebip of Turkish Academy of Sciences The author is supported by the Distinguished Young Scholar Award, Tuba-Gebip of Turkish Academy of Sciences.
dc.description.volume131
dc.identifier.doi10.1016/j.jnt.2011.02.013
dc.identifier.eissn1096-1658
dc.identifier.issn0022-314X
dc.identifier.quartileQ3
dc.identifier.scopus2-s2.0-79953751434
dc.identifier.urihttps://doi.org/10.1016/j.jnt.2011.02.013
dc.identifier.urihttps://hdl.handle.net/20.500.14288/7660
dc.identifier.wos290071000010
dc.keywordsL-functions
dc.keywordsSpecial values
dc.keywordsJordan's totient function
dc.keywordsEuler's totient function
dc.keywordsMean square average
dc.keywordsGauss sums
dc.keywordsRamanujan sums
dc.language.isoeng
dc.publisherAcademic Press Inc Elsevier Science
dc.relation.ispartofJournal of Number Theory
dc.subjectMathematics
dc.titleOn the mean square average of special values of L-functions
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorAlkan, Emre
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
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relation.isOrgUnitOfPublication.latestForDiscovery2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
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