dc.contributor.advisor | Papanikolas, Matthew | |
dc.creator | Lutes, Brad Aubrey | |
dc.date.accessioned | 2010-10-12T22:31:45Z | |
dc.date.accessioned | 2010-10-14T16:07:24Z | |
dc.date.available | 2010-10-12T22:31:45Z | |
dc.date.available | 2010-10-14T16:07:24Z | |
dc.date.created | 2010-08 | |
dc.date.issued | 2010-10-12 | |
dc.date.submitted | August 2010 | |
dc.identifier.uri | https://hdl.handle.net/1969.1/ETD-TAMU-2010-08-8251 | |
dc.description.abstract | Let 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 |
dc.format.mimetype | application/pdf | |
dc.language.iso | en_US | |
dc.subject | Function Fields | en |
dc.subject | Drinfeld Modules | en |
dc.subject | L-functions | en |
dc.title | Special Values of the Goss L-function and Special Polynomials | en |
dc.type | Book | en |
dc.type | Thesis | en |
thesis.degree.department | Mathematics | en |
thesis.degree.discipline | Mathematics | en |
thesis.degree.grantor | Texas A&M University | en |
thesis.degree.name | Doctor of Philosophy | en |
thesis.degree.level | Doctoral | en |
dc.contributor.committeeMember | Rojas, J. Maurice | |
dc.contributor.committeeMember | Tretkoff, Paula | |
dc.contributor.committeeMember | Dahm, P. Fred | |
dc.type.genre | Electronic Dissertation | en |
dc.type.material | text | en |