Please use this identifier to cite or link to this item: http://hdl.handle.net/10603/426759
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dc.date.accessioned2022-12-17T10:57:44Z-
dc.date.available2022-12-17T10:57:44Z-
dc.identifier.urihttp://hdl.handle.net/10603/426759-
dc.description.abstractIn the first part of the talk we would discuss a topic about the Fourier coefficients of modular forms. Namely, we would focus on the question of distinguishing two modular forms by certain arithmetically interesting Fourier coefficients. These type of results are known as recognition results and have been a useful theme in the theory of modular forms, having lots of applications. As an example we would recall the Sturm s bound (which applies quite generally to a wide class of modular forms), which says that two modular forms are equal if (in a suitable sense) their first few Fourier coefficients agree. As another example we would mention the classical multiplicity-one result for elliptic newforms of integral weight, which says that if two such forms f1, f2 have the same eigenvalues of the p-th Hecke operator Tp for almost all primes p, then f1 = f2. The heart of the first part of the talk would concentrate on Hermitian cusp forms of degree 2. These objects have a Fourier expansion indexed by certain matrices of size 2 over an imaginary quadratic field. We show that Hermitian cusp forms of weight k for the Hermitian modular group of degree 2 are determined by their Fourier coe cients indexed by matrices whose determinants are essentially square free. Moreover, we give a quantitative version of the above result. is is a consequence of the corresponding results for integral weight elliptic cusp forms, which will also be discussed. is result was established by A. Saha in the context of Siegel modular forms and played a crucial role (among others) in the automorphic transfer from GSp(4) to GL(4). We expect similar applications. We also discuss few results on the square free Fourier coefficients of elliptic cusp forms. In the second part of the talk we introduce Saito Kurokawa lifts: these are certain Siegel modular forms li ed from classical elliptic modular forms on the upper half plane H...
dc.format.extentxii, 87 p.
dc.languageEnglish
dc.relation
dc.rightsuniversity
dc.titleFourier coeffcients of modular forms and mass of pullbacks of Saito Kurokawa lifts
dc.title.alternativeFourier coeffcients of modular forms and mass of pullbacks of Saito Kurokawa lifts
dc.creator.researcherPramath, A V
dc.subject.keywordMathematics
dc.subject.keywordPhysical Sciences
dc.description.note
dc.contributor.guideDas, Soumya
dc.publisher.placeBangalore
dc.publisher.universityIndian Institute of Science Bangalore
dc.publisher.institutionMathematics
dc.date.registered
dc.date.completed2019
dc.date.awarded2019
dc.format.dimensions30 cm.
dc.format.accompanyingmaterialNone
dc.source.universityUniversity
dc.type.degreePh.D.
Appears in Departments:Mathematics

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01_title.pdfAttached File254.02 kBAdobe PDFView/Open
02_prelim pages.pdf268.35 kBAdobe PDFView/Open
03_table of contents.pdf435.5 kBAdobe PDFView/Open
04_abstract.pdf426.85 kBAdobe PDFView/Open
05_chapter 1.pdf482.32 kBAdobe PDFView/Open
06_chapter 2.pdf484.92 kBAdobe PDFView/Open
07_chapter 3.pdf462.05 kBAdobe PDFView/Open
08_chapter 4.pdf541.52 kBAdobe PDFView/Open
09_chapter 5.pdf567.49 kBAdobe PDFView/Open
10_chapter 6.pdf481.99 kBAdobe PDFView/Open
80_recommendation.pdf760.02 kBAdobe PDFView/Open


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