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dc.contributor.advisorPapanikolas, Matthewen_US
dc.creatorLutes, Brad Aubreyen_US
dc.date.accessioned2010-10-12T22:31:45Zen_US
dc.date.accessioned2010-10-14T16:07:24Z
dc.date.available2010-10-12T22:31:45Zen_US
dc.date.available2010-10-14T16:07:24Z
dc.date.created2010-08en_US
dc.date.issued2010-10-12en_US
dc.date.submittedAugust 2010en_US
dc.identifier.urihttp://hdl.handle.net/1969.1/ETD-TAMU-2010-08-8251en_US
dc.description.abstractLet K be the function field of an irreducible, smooth projective curve X defined over Fq. Let [lemniscate] be a fixed point on X and let A [a subset of or is equal to] K be the Dedekind domain of functions which are regular away from [lemniscate]. Following the work of Greg Anderson, we define special polynomials and explain how they are used to define an A-module (in the case where the class number of A and the degree of [lemniscate] are both one) known as the module of special points associated to the Drinfeld A-module [rho]. We show that this module is finitely generated and explicitly compute its rank. We also show that if K is a function field such that the degree of [lemniscate] is one, then the Goss L-function, evaluated at 1, is a finite linear combination of logarithms evaluated at algebraic points. We conclude with examples showing how to use special polynomials to compute special values of both the Goss L-function and the Goss zeta function.en_US
dc.format.mimetypeapplication/pdfen_US
dc.language.isoen_USen_US
dc.subjectFunction Fieldsen_US
dc.subjectDrinfeld Modulesen_US
dc.subjectL-functionsen_US
dc.titleSpecial Values of the Goss L-function and Special Polynomialsen_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.committeeMemberRojas, J. Mauriceen_US
dc.contributor.committeeMemberTretkoff, Paulaen_US
dc.contributor.committeeMemberDahm, P. Freden_US
dc.type.genreElectronic Dissertationen_US
dc.type.materialtexten_US


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