Publication:
Equidistribution of signs for modular eigenforms of half integral weight

dc.contributor.authorWiese, Gabor
dc.contributor.buuauthorİnam, İlker
dc.contributor.departmentFen Edebiyat Fakültesi
dc.contributor.departmentMatematik Bölümü
dc.contributor.scopusid25925069700
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.
dc.description.sponsorshipGerman Research Foundation (DFG)
dc.description.sponsorshipLuxembourg National Research Fund
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.
dc.identifier.endpage339
dc.identifier.issn0003-889X
dc.identifier.issn1420-8938
dc.identifier.issue4
dc.identifier.scopus2-s2.0-84885809066
dc.identifier.startpage331
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.volume101
dc.identifier.wos000325771000004
dc.indexed.wosSCIE
dc.language.isoen
dc.publisherSpringer
dc.relation.collaborationYurt dışı
dc.relation.journalArchiv der Mathematik
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi
dc.relation.tubitakTÜBİTAK
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectMathematics
dc.subjectForms of half-integer weight
dc.subjectShimura lift
dc.subjectFourier coefficients of automorphic forms
dc.subjectSato-Tate equidistribution
dc.subjectFourier coefficients
dc.subjectElliptic-curves
dc.subjectSelmer groups
dc.subjectForms
dc.subjectValues
dc.subject.scopusCusp Form; L-Function; Fourier Coefficients
dc.subject.wosMathematics
dc.titleEquidistribution of signs for modular eigenforms of half integral weight
dc.typeArticle
dc.wos.quartileQ3
dspace.entity.typePublication
local.contributor.departmentFen Edebiyat Fakültesi/Matematik Bölümü
local.indexed.atScopus
local.indexed.atWOS

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