Algebraic modular forms on definite orthogonal groups
Abstract/Contents
- Abstract
- The present thesis examines explicit computation with modular forms on definite orthogonal groups over the rational numbers. The space of functions on the genus of a definite quadratic form affords a natural representation of the Hecke algebra, which realizes the function space as a space of modular forms. The algorithm of the thesis computes the genus of a quadratic form as well as Hecke operators on the associated space of modular forms. A formula derived in the thesis yields Satake parameters from Hecke eigenvalues. Explicit examples of Satake parameters verify the correctness of the algorithm and the formula by their agreement with the predictions of the Arthur conjectures.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2013 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Murphy, Daniel Kim |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Venkatesh, Akshay, 1981- |
| Thesis advisor | Venkatesh, Akshay, 1981- |
| Thesis advisor | Bump, Daniel, 1952- |
| Thesis advisor | Conrad, Brian, 1970- |
| Advisor | Bump, Daniel, 1952- |
| Advisor | Conrad, Brian, 1970- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Daniel Kim Murphy. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2013. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2013 by Daniel Kim Murphy
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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