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dc.contributor.advisorThakur, Dineshen
dc.contributor.authorTodd, George
dc.creatorTodd, Georgeen
dc.date.accessioned2015-06-12T17:37:22Zen
dc.date.available2015-06-12T17:37:22Zen
dc.date.issued2015en
dc.identifier.urihttp://hdl.handle.net/10150/556863en
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.
dc.language.isoen_USen
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.subjectMathematicsen
dc.titleLinear Relations between Multizeta Valuesen_US
dc.typetexten
dc.typeElectronic Dissertationen
thesis.degree.grantorUniversity of Arizonaen
thesis.degree.leveldoctoralen
dc.contributor.committeememberJoshi, Kirtien
dc.contributor.committeememberCais, Brydenen
dc.contributor.committeememberThakur, Dineshen
dc.contributor.committeememberLux, Klausen
dc.description.releaseRelease after 8-May-2016en
thesis.degree.disciplineGraduate Collegeen
thesis.degree.disciplineMathematicsen
thesis.degree.namePh.D.en
refterms.dateFOA2016-05-08T00:00:00Z
html.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.


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