Equidistribution of signs for modular eigenforms of half integral weight

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dc.contributor.authorWiese, Gabor
dc.contributor.buuauthorİnam, İlker
dc.contributor.departmentUludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.tr_TR
dc.contributor.scopusid25925069700tr_TR
dc.date.accessioned2022-12-09T05:42:25Z
dc.date.available2022-12-09T05:42:25Z
dc.date.issued2013-10-08
dc.description.abstractLet f be a cusp form of weight k + 1/2 and at most quadratic nebentype character whose Fourier coefficients a(n) are all real. We study an equidistribution conjecture of Bruinier and Kohnen for the signs of a(n). We prove this conjecture for certain subfamilies of coefficients that are accessible via the Shimura lift by using the Sato-Tate equidistribution theorem for integral weight modular forms. Firstly, an unconditional proof is given for the family {a(tp (2))} (p) , where t is a squarefree number and p runs through the primes. In this case, the result is in terms of natural density. To prove it for the family {a(tn (2))} (n) where t is a squarefree number and n runs through all natural numbers, we assume the existence of a suitable error term for the convergence of the Sato-Tate distribution, which is weaker than one conjectured by Akiyama and Tanigawa. In this case, the results are in terms of Dedekind-Dirichlet density.en_US
dc.description.sponsorshipGerman Research Foundation (DFG)en_US
dc.description.sponsorshipLuxembourg National Research Funden_US
dc.identifier.citationİnam, İ. ve Wiese, G. (2013). "Equidistribution of signs for modular eigenforms of half integral weight". Archiv der Mathematik, 101(4), 331-339.en_US
dc.identifier.endpage339tr_TR
dc.identifier.issn0003-889X
dc.identifier.issn1420-8938
dc.identifier.issue4tr_TR
dc.identifier.scopus2-s2.0-84885809066tr_TR
dc.identifier.startpage331tr_TR
dc.identifier.urihttps://doi.org/10.1007/s00013-013-0566-4
dc.identifier.urihttps://link.springer.com/article/10.1007/s00013-013-0566-4
dc.identifier.urihttp://hdl.handle.net/11452/29777
dc.identifier.volume101tr_TR
dc.identifier.wos000325771000004tr_TR
dc.indexed.scopusScopusen_US
dc.indexed.wosSCIEen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.collaborationYurt dışıtr_TR
dc.relation.journalArchiv der Mathematiken_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergitr_TR
dc.relation.tubitakTÜBİTAKtr_TR
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectMathematicsen_US
dc.subjectForms of half-integer weighten_US
dc.subjectShimura liften_US
dc.subjectFourier coefficients of automorphic formsen_US
dc.subjectSato-Tate equidistributionen_US
dc.subjectFourier coefficientsen_US
dc.subjectElliptic-curvesen_US
dc.subjectSelmer groupsen_US
dc.subjectFormsen_US
dc.subjectValuesen_US
dc.subject.scopusCusp Form; L-Function; Fourier Coefficientsen_US
dc.subject.wosMathematicsen_US
dc.titleEquidistribution of signs for modular eigenforms of half integral weighten_US
dc.typeArticle
dc.wos.quartileQ3en_US

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