Hypergeometric functions in arithmetic geometry

dc.contributor.advisorVillegas, Fernando Rodriguezen
dc.creatorSalerno, Adriana Julia, 1979-en
dc.date.accessioned2012-10-16T18:26:27Zen
dc.date.accessioned2017-05-11T22:28:49Z
dc.date.available2012-10-16T18:26:27Zen
dc.date.available2017-05-11T22:28:49Z
dc.date.issued2009-05en
dc.descriptiontexten
dc.description.abstractHypergeometric functions seem to be ubiquitous in mathematics. In this document, we present a couple of ways in which hypergeometric functions appear in arithmetic geometry. First, we show that the number of points over a finite field [mathematical symbol] on a certain family of hypersurfaces, [mathematical symbol] ([lamda]), is a linear combination of hypergeometric functions. We use results by Koblitz and Gross to find explicit relationships, which could be useful for computing Zeta functions in the future. We then study more geometric aspects of the same families. A construction of Dwork's gives a vector bundle of deRham cohomologies equipped with a connection. This connection gives rise to a differential equation which is known to be hypergeometric. We developed an algorithm which computes the parameters of the hypergeometric equations given the family of hypersurfaces.en
dc.description.departmentMathematicsen
dc.format.mediumelectronicen
dc.identifier.urihttp://hdl.handle.net/2152/18410en
dc.language.isoengen
dc.rightsCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en
dc.subject.lcshHypergeometric functionsen
dc.subject.lcshArithmetical algebraic geometryen
dc.subject.lcshHypersurfacesen
dc.titleHypergeometric functions in arithmetic geometryen

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