arXiv subjects

W. Dale Brownawell

Publications and source records attributed to W. Dale Brownawell.

4 recordsLinked to original sources

arXiv2022

Function Field Analogue of Shimura's Conjecture on Period Symbols

In this paper we introduce the notion of Shimura's period symbols over function fields in positive characteristic and establish their fundamental properties. We further formulate and prove a function field analogue of Shimura's conjecture on the algebraic independence of period symbols. Our results enable us to verify the algebraic independence of the coordinates of any nonzero period vector of an abelian t-module with complex multiplication whose CM type is non-degenerate and defined over an algebraic function field. This is an extension of Yu's work on Hilbert-Blumenthal t-modules.

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arXiv2018

A rapid introduction to Drinfeld modules, $t$-modules, and $t$-motives

The present article aims to provide a brief account of the theories of Drinfeld modules and Anderson's $t$-modules and $t$-motives. As such the article is not meant to be comprehensive, but we have endeavored to summarize aspects of the theory that are of current interest and to include a number of examples.

math.NT↗

arXiv2002

Determination of the algebraic relations among special Gamma-values in positive characteristic

We devise a new criterion for linear independence over function fields. Using this tool in the setting of dual t-motives, we find that all algebraic relations among special values of the geometric function field Gamma-function are explained by the standard functional equations.

math.NT↗

arXiv2001

Linear independence of Gamma values in positive characteristic

We investigate the arithmetic nature of special values of Thakur's function field Gamma function at rational points. Our main result is that all linear independence relations over the field of algebraic functions are consequences of the known relations of Anderson and Thakur arising from the functional equations of the Gamma function.

math.NT↗