Persistent Link:
http://hdl.handle.net/10150/556863
Title:
Linear Relations between Multizeta Values
Author:
Todd, George
Issue Date:
2015
Publisher:
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-2016
Abstract:
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:
text; Electronic Dissertation
Keywords:
Mathematics
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Thakur, Dinesh

Full metadata record

DC FieldValue Language
dc.language.isoen_USen
dc.titleLinear Relations between Multizeta Valuesen_US
dc.creatorTodd, Georgeen
dc.contributor.authorTodd, Georgeen
dc.date.issued2015en
dc.publisherThe University of Arizona.en
dc.rightsCopyright © 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.en
dc.description.releaseRelease after 8-May-2016en
dc.description.abstractIn 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.en
dc.typetexten
dc.typeElectronic Dissertationen
dc.subjectMathematicsen
thesis.degree.namePh.D.en
thesis.degree.leveldoctoralen
thesis.degree.disciplineGraduate Collegeen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorUniversity of Arizonaen
dc.contributor.advisorThakur, Dineshen
dc.contributor.committeememberJoshi, Kirtien
dc.contributor.committeememberCais, Brydenen
dc.contributor.committeememberThakur, Dineshen
dc.contributor.committeememberLux, Klausen
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