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dc.contributor.advisorSharifi, Romyar T.en
dc.contributor.authorMa, Dingen
dc.creatorMa, Dingen
dc.date.accessioned2016-06-14T19:37:01Z
dc.date.available2016-06-14T19:37:01Z
dc.date.issued2016
dc.identifier.urihttp://hdl.handle.net/10150/613133
dc.description.abstractThis thesis explores various connections between multiple zeta values and modular forms of low level. In the first part, we consider double zeta values of odd weight. We generalize a result of Gangl, Kaneko and Zagier on period polynomial relations among double zeta values of even weights to this setting. This answers a question asked by Zagier. We also prove a conjecture of Zagier on the inverse of a certain matrix in this setting. In the second part, we study multiple zeta values of higher depth. In particular, we give a criterion and a conjectural criterion for "fake" relations in depth 4. In the last part, we consider multiple zeta values of levels 2 and 3. We describe one connection with the Hecke operators T₂ and T₃, and another connection with newforms of level 2 and 3. We also give a conjectural generalization of the Eichler-Shimura-Manin correspondence to the spaces of newforms of levels 2 and 3.
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.subjectmodular formen
dc.subjectmultiple zeta valueen
dc.subjectperiod polynomialen
dc.subjectMathematicsen
dc.subjectHecke operatoren
dc.titleRelations among Multiple Zeta Values and Modular Forms of Low Levelen_US
dc.typetexten
dc.typeElectronic Dissertationen
thesis.degree.grantorUniversity of Arizonaen
thesis.degree.leveldoctoralen
dc.contributor.committeememberCais, Bryden R.en
dc.contributor.committeememberJoshi, Kirti N.en
dc.contributor.committeememberTiep, Pham Huuen
dc.contributor.committeememberSharifi, Romyar T.en
thesis.degree.disciplineGraduate Collegeen
thesis.degree.disciplineMathematicsen
thesis.degree.namePh.D.en
refterms.dateFOA2018-09-11T12:57:11Z
html.description.abstractThis thesis explores various connections between multiple zeta values and modular forms of low level. In the first part, we consider double zeta values of odd weight. We generalize a result of Gangl, Kaneko and Zagier on period polynomial relations among double zeta values of even weights to this setting. This answers a question asked by Zagier. We also prove a conjecture of Zagier on the inverse of a certain matrix in this setting. In the second part, we study multiple zeta values of higher depth. In particular, we give a criterion and a conjectural criterion for "fake" relations in depth 4. In the last part, we consider multiple zeta values of levels 2 and 3. We describe one connection with the Hecke operators T₂ and T₃, and another connection with newforms of level 2 and 3. We also give a conjectural generalization of the Eichler-Shimura-Manin correspondence to the spaces of newforms of levels 2 and 3.


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