Author
Todd, GeorgeIssue Date
2015Keywords
MathematicsAdvisor
Thakur, Dinesh
Metadata
Show full item recordPublisher
The University of Arizona.Rights
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.Embargo
Release after 8-May-2016Abstract
In this dissertation, we discuss F(q)(t)-linear relations beteen the multizeta values in function fields defined by Thakur. He proved that the product of multizeta values is a $\mathbb{F}_p$-linear combination of multizeta values of the same weight analagous to the classical stuffle product for classical multizeta values. However, there is no known analog of the shuffle product for Thakur multizeta values from which to derive F(q)(t)-linear relations. In this work, we introduce several families of maps between the space of relations of the power sums from which the multizeta values are defined. We describe the F(q)(t)-linear relations currently in the literature in terms of these maps and provide many new relations. The main results of the dissertation are a conjectural characterization of all F(q)(t)-linear relations between Thakur multizeta values as well as the dimension of the F(q)(t)-span of multizeta values of a fixed weight, in addition to proving several cases under which the two are equivalent. These two conjectures provide the function field analog of the conjectures provided by Zagier and others dealing with similar issues for the classical multizeta values.Type
textElectronic Dissertation
Degree Name
Ph.D.Degree Level
doctoralDegree Program
Graduate CollegeMathematics