Relations among Multiple Zeta Values and Modular Forms of Low Level

Persistent Link:
http://hdl.handle.net/10150/613133
Title:
Relations among Multiple Zeta Values and Modular Forms of Low Level
Author:
Ma, Ding
Issue Date:
2016
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.
Abstract:
This 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.
Type:
text; Electronic Dissertation
Keywords:
modular form; multiple zeta value; period polynomial; Mathematics; Hecke operator
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Sharifi, Romyar T.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen
dc.titleRelations among Multiple Zeta Values and Modular Forms of Low Levelen_US
dc.creatorMa, Dingen
dc.contributor.authorMa, Dingen
dc.date.issued2016-
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.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.en
dc.typetexten
dc.typeElectronic Dissertationen
dc.subjectmodular formen
dc.subjectmultiple zeta valueen
dc.subjectperiod polynomialen
dc.subjectMathematicsen
dc.subjectHecke operatoren
thesis.degree.namePh.D.en
thesis.degree.leveldoctoralen
thesis.degree.disciplineGraduate Collegeen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorUniversity of Arizonaen
dc.contributor.advisorSharifi, Romyar T.en
dc.contributor.committeememberCais, Bryden R.en
dc.contributor.committeememberJoshi, Kirti N.en
dc.contributor.committeememberTiep, Pham Huuen
dc.contributor.committeememberSharifi, Romyar T.en
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