Construction of modular forms with Poincaré series

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buir.advisorYeşilyurt, Hamza
dc.contributor.authorGüneş, Çisem
dc.date.accessioned2016-01-08T18:12:48Z
dc.date.available2016-01-08T18:12:48Z
dc.date.issued2010
dc.departmentDepartment of Mathematicsen_US
dc.descriptionAnkara : The Department of Mathematics and the Institute of Engineering and Science of Bilkent University, 2010.en_US
dc.descriptionThesis (Master's) -- Bilkent University, 2010.en_US
dc.descriptionIncludes bibliographical references leaves 63-65.en_US
dc.description.abstractIn this thesis, we construct holomorphic modular forms of integral weight k > 2 for the principle congruence subgroup Γ( ¯ N) by means of Poincar´e series. We start by providing the necessary background information on modular forms. Then, we show that Poincar´e series are in fact holomorphic modular forms and we obtain explicit formulas for their Fourier coefficients. For the special case when Poincar´e series are Eisenstein series, their Fourier coefficients become relatively simple. We give Fourier coefficients of the Eisenstein series belonging to the principle congruence subgroup. Finally, as an application of what has been studied, we construct Eisenstein series for the Hecke congruence supgroup.en_US
dc.description.degreeM.S.en_US
dc.description.statementofresponsibilityGüneş, Çisemen_US
dc.format.extentvii, 65 leavesen_US
dc.identifier.itemidB122453
dc.identifier.urihttp://hdl.handle.net/11693/15070
dc.language.isoEnglishen_US
dc.publisherBilkent Universityen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectPoincar´e seriesen_US
dc.subjectCongruence subgroupsen_US
dc.subjectModular groupen_US
dc.subjectCusp formsen_US
dc.subjectModular formsen_US
dc.subjectEisenstein seriesen_US
dc.subject.lccQA243 .G85 2010en_US
dc.subject.lcshForms, Modular.en_US
dc.subject.lcshPoincaré series.en_US
dc.titleConstruction of modular forms with Poincaré seriesen_US
dc.typeThesisen_US
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