Arithmetic properties of coefficients of L-functions of elliptic curves

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dc.contributor.authorGuloglu, Ahmet M.
dc.contributor.authorLuca, Florian
dc.contributor.authorYalciner, Aynur
dc.date.accessioned2020-03-26T19:52:56Z
dc.date.available2020-03-26T19:52:56Z
dc.date.issued2018
dc.departmentSelçuk Üniversitesien_US
dc.description.abstractLet n = 1 ann -s be the L-series of an elliptic curve E defined over the rationals without complex multiplication. In this paper, we present certain similarities between the arithmetic properties of the coefficients {an}8 n= 1 and Euler's totient function.(n). Furthermore, we prove that both the set of n such that the regular polygon with | an| sides is ruler-and-compass constructible, and the set of n such that n-an + 1 =.(n) have asymptotic density zero. Finally, we improve a bound of Luca and Shparlinski on the counting function of elliptic pseudoprimes.en_US
dc.description.sponsorshipScientific and Technological Research Council of TurkeyTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [114F404]; NRF of South Africa [CPRR160325161141]; A-rated scientist award from NRF of South Africa; Czech Granting Agency [17-02804S]en_US
dc.description.sponsorshipThe first author is supported by the Scientific and Technological Research Council of Turkey [114F404]. The second author was partially supported by Grant CPRR160325161141 and an A-rated scientist award both from the NRF of South Africa and by Grant No. 17-02804S of the Czech Granting Agency.en_US
dc.identifier.doi10.1007/s00605-018-1175-xen_US
dc.identifier.endpage273en_US
dc.identifier.issn0026-9255en_US
dc.identifier.issn1436-5081en_US
dc.identifier.issue2en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage247en_US
dc.identifier.urihttps://dx.doi.org/10.1007/s00605-018-1175-x
dc.identifier.urihttps://hdl.handle.net/20.500.12395/36346
dc.identifier.volume187en_US
dc.identifier.wosWOS:000443569700004en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSPRINGER WIENen_US
dc.relation.ispartofMONATSHEFTE FUR MATHEMATIKen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.selcuk20240510_oaigen_US
dc.subjectRational elliptic curvesen_US
dc.subjectChebotarev Density Theoremen_US
dc.subjectArithmetic functionsen_US
dc.subjectL-functionsen_US
dc.subjectEuler's totient functionen_US
dc.subjectElliptic pseudoprimesen_US
dc.titleArithmetic properties of coefficients of L-functions of elliptic curvesen_US
dc.typeArticleen_US

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