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.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/613133 |
| Date | January 2016 |
| Creators | Ma, Ding |
| Contributors | Sharifi, Romyar T., Cais, Bryden R., Joshi, Kirti N., Tiep, Pham Huu, Sharifi, Romyar T. |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Electronic Dissertation |
| 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. |
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