An Explicit Theta Lift from Hilbert to Siegel Paramodular Forms
Rupert, Malcolm Edward. (2017). An Explicit Theta Lift from Hilbert to Siegel Paramodular Forms. Theses and Dissertations Collection, University of Idaho Library Digital Collections. https://www.lib.uidaho.edu/digital/etd/items/rupert_idaho_0089e_11113.html
- Title:
- An Explicit Theta Lift from Hilbert to Siegel Paramodular Forms
- Author:
- Rupert, Malcolm Edward
- Date:
- 2017
- Keywords:
- Automorphic forms Hilbert Modular forms Paramodular forms Theta Lift
- Program:
- Mathematics
- Subject Category:
- Mathematics
- Abstract:
-
Let E/L be a real quadratic extension of number fields. This dissertation contains the construction of an explicit map from an irreducible cuspidal automorphic representation of GL(2,E) which contains a Hilbert modular form with Gamma_0 level to an irreducible automorphic representation of GSP(4,L) which contains a Siegel paramodular form. We discuss how to construct an orthogonal representation from a character and a representation of a quaternion algebra, in some generality. There is a well known global theta correspondence for the pair (GSO(4), GSP(4)). We discuss the local theta correspondence and discuss its invariance properties. Finally, we exhibit local data which produces a paramodular invariant vector for the local theta lift at every place, except when the local extension has wild ramification.
- Description:
- doctoral, Ph.D., Mathematics -- University of Idaho - College of Graduate Studies, 2017
- Major Professor:
- Johnson-Leung, Jennifer
- Committee:
- Roberts, Brooks; Woo, Alexander; Baumgaertner, Bert
- Defense Date:
- 2017
- Identifier:
- Rupert_idaho_0089E_11113
- Type:
- Text
- Format Original:
- Format:
- application/pdf
- Rights:
- In Copyright - Educational Use Permitted. For more information, please contact University of Idaho Library Special Collections and Archives Department at libspec@uidaho.edu.
- Standardized Rights:
- http://rightsstatements.org/vocab/InC-EDU/1.0/