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dc.contributor.advisorPapanikolas, Matthewen_US
dc.creatorFuselier, Jenny G.en_US
dc.date.accessioned2010-01-15T00:01:45Zen_US
dc.date.accessioned2010-01-16T01:54:24Z
dc.date.available2010-01-15T00:01:45Zen_US
dc.date.available2010-01-16T01:54:24Z
dc.date.created2007-08en_US
dc.date.issued2009-05-15en_US
dc.identifier.urihttp://hdl.handle.net/1969.1/ETD-TAMU-1547
dc.description.abstractThe theory of hypergeometric functions over finite fields was developed in the mid- 1980s by Greene. Since that time, connections between these functions and elliptic curves and modular forms have been investigated by mathematicians such as Ahlgren, Frechette, Koike, Ono, and Papanikolas. In this dissertation, we begin by giving a survey of these results and introducing hypergeometric functions over finite fields. We then focus on a particular family of elliptic curves whose j-invariant gives an automorphism of P1. We present an explicit relationship between the number of points on this family over Fp and the values of a particular hypergeometric function over Fp. Then, we use the same family of elliptic curves to construct a formula for the traces of Hecke operators on cusp forms in level 1, utilizing results of Hijikata and Schoof. This leads to formulas for Ramanujan’s -function in terms of hypergeometric functions.en_US
dc.format.mediumelectronicen_US
dc.format.mimetypeapplication/pdfen_US
dc.language.isoen_USen_US
dc.subjecthypergeometricen_US
dc.subjectmodular formsen_US
dc.subjectelliptic curvesen_US
dc.subjectRamanujanen_US
dc.titleHypergeometric functions over finite fields and relations to modular forms and elliptic curvesen_US
dc.typeBooken
dc.typeThesisen
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorTexas A&M Universityen_US
thesis.degree.nameDoctor of Philosophyen_US
thesis.degree.levelDoctoralen_US
dc.contributor.committeeMemberKlappenecker, Andreasen_US
dc.contributor.committeeMemberStiller, Peteren_US
dc.contributor.committeeMemberTretkoff, Paulaen_US
dc.type.genreElectronic Dissertationen_US
dc.type.materialtexten_US
dc.format.digitalOriginborn digitalen_US


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