MAASS SPACE FOR LIFTING TO GL(2,B) OVER A DIVISION QUATERNION ALGEBRA

Wagh, Siddhesh

MAASS SPACE FOR LIFTING TO GL(2,B) OVER A DIVISION QUATERNION ALGEBRA

dc.contributor.advisor	Pitale, Ameya
dc.contributor.author	Wagh, Siddhesh
dc.contributor.committeeMember	Schmidt, Ralf
dc.contributor.committeeMember	Parthasarathy, Ramkumar
dc.contributor.committeeMember	Przebinda, Tomasz
dc.contributor.committeeMember	Roche, Alan
dc.date.accessioned	2019-08-08T20:10:29Z
dc.date.available	2019-08-08T20:10:29Z
dc.date.issued	2019-08-01
dc.date.manuscript	2019-07-25
dc.description.abstract	Muto, Narita and Pitale construct counterexamples to the Generalized Ramanujan Conjecture for GL(2,B) over the division quaternion algebra B with discriminant two via a lift from SL(2). In this dissertation, I characterize the image of this lift in terms of the Fourier coefficients. The previous methods of Maass, Kohnen or Kojima do not apply here, hence I approached this problem via a combination of classical and representation theory techniques to identify the image. Crucially, I used the Jacquet Langlands correspondence described by Badulescu and Renard to characterize the representations.	en_US
dc.identifier.uri	https://hdl.handle.net/11244/321131
dc.language	en	en_US
dc.rights	Attribution-ShareAlike 4.0 International	*
dc.rights.uri	http://creativecommons.org/licenses/by-sa/4.0/	*
dc.subject	Number Theory	en_US
dc.subject	Automorphic forms	en_US
dc.subject	Representation Theory	en_US
dc.subject	Maass forms	en_US
dc.thesis.degree	Ph.D.	en_US
dc.title	MAASS SPACE FOR LIFTING TO GL(2,B) OVER A DIVISION QUATERNION ALGEBRA	en_US
ou.group	College of Arts and Sciences::Department of Mathematics	en_US
shareok.orcid	0000-0002-9415-0880	en_US