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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2010-08-8251 |
| Date | 2010 August 1900 |
| Creators | Lutes, Brad Aubrey |
| Contributors | Papanikolas, Matthew |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | application/pdf |
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