p-adic Differential Operators on Automorphic Forms and Applications.
dc.contributor.author | Eischen, Ellen E. | en_US |
dc.date.accessioned | 2009-09-03T14:55:59Z | |
dc.date.available | NO_RESTRICTION | en_US |
dc.date.available | 2009-09-03T14:55:59Z | |
dc.date.issued | 2009 | en_US |
dc.date.submitted | en_US | |
dc.identifier.uri | https://hdl.handle.net/2027.42/63860 | |
dc.description.abstract | We construct certain C ∞-differential operators and their p-adic analogues, which act on (vector- or scalar-valued) automorphic forms on the unitary groups U (n, n). We study properties of these operators, and we prove some arithmeticity theorems using them. These differential operators are a generalization to the p-adic case of the C ∞-differential operators first studied by H. Maass and later studied extensively by M. Harris and G. Shimura. They are a generalization to the vector-valued situation of the p-adic differential operators constructed in the one-dimensional setting by N. Katz. They should be useful in the construction of certain p-adic L-functions, in particular p-adic L-functions attached to p-adic families of automorphic forms on the unitary groups U (n) × U (n). | en_US |
dc.format.extent | 1171869 bytes | |
dc.format.extent | 1373 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | en_US |
dc.subject | Differential Operators | en_US |
dc.subject | Automorphic Forms | en_US |
dc.subject | P-adic Automorphic Forms | en_US |
dc.subject | P-adic Differential Operators | en_US |
dc.subject | Gauss-Manin Connection | en_US |
dc.subject | Arithmeticity | en_US |
dc.title | p-adic Differential Operators on Automorphic Forms and Applications. | en_US |
dc.type | Thesis | en_US |
dc.description.thesisdegreename | PhD | en_US |
dc.description.thesisdegreediscipline | Mathematics | en_US |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | en_US |
dc.contributor.committeemember | Ramsey, Nicholas Adam | en_US |
dc.contributor.committeemember | Skinner, Christopher M. | en_US |
dc.contributor.committeemember | Mustata, Mircea Immanuel | en_US |
dc.contributor.committeemember | Strauss, Martin | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/63860/1/eeischen_1.pdf | |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
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