Arithmetic of the Asai L-function for Hilbert Modular Forms.
dc.contributor.author | Kaye, Adam Rubin | |
dc.date.accessioned | 2016-06-10T19:30:35Z | |
dc.date.available | NO_RESTRICTION | |
dc.date.available | 2016-06-10T19:30:35Z | |
dc.date.issued | 2016 | |
dc.date.submitted | 2016 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/120693 | |
dc.description.abstract | Arithmetic of the Asai L-function for Hilbert modular forms Adam Kaye Chair: Kartik Prassanna We prove two results on rationality of special values of the Asai L-function attached to Hilbert modular forms at critical points. Such L-functions only admit critical values when the Hilbert modular form has non-parallel weight. Our rationality results generalize previous work of Shimura on algebraicity. The first result uses a period defined by transferring the Hilbert modular form to a Shimura curve. The second result uses a period defined using rational structures on the coherent cohomology of Hilbert modular surfaces. We also give some partial results towards integrality of such L-values. Our results are motivated by the study of a p-adic analog of the Beilinson conjecture, which is a deep conjecture relating algebraic cycles (and motivic cohomology) to values of L-functions. | |
dc.language.iso | en_US | |
dc.subject | Number Theory | |
dc.subject | L-functions | |
dc.subject | Hilbert modular forms | |
dc.subject | Special values of L-functions | |
dc.subject | Beilinson's Conjecture | |
dc.title | Arithmetic of the Asai L-function for Hilbert Modular Forms. | |
dc.type | Thesis | en_US |
dc.description.thesisdegreename | PhD | |
dc.description.thesisdegreediscipline | Mathematics | |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | |
dc.contributor.committeemember | Prasanna, Kartik | |
dc.contributor.committeemember | Strauss, Martin | |
dc.contributor.committeemember | Snowden, Andrew | |
dc.contributor.committeemember | Lagarias, Jeffrey C | |
dc.contributor.committeemember | Debacker, Stephen M | |
dc.subject.hlbsecondlevel | Mathematics | |
dc.subject.hlbtoplevel | Science | |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/120693/1/adamkaye_1.pdf | |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.