Fields of rationality of cuspidal automorphic representations

This thesis examines questions related to the growth of fields of rationality of cuspidal automorphic representations in families. Specifically, if F is a family of cuspidal automorphic representations with fixed central character, prescribed behavior at the Archimedean places, and such that the finite component [pi] [infinity] has a [Gamma]-fixed vector, we expect the proportion of [pi] [epsilon] F with bounded field of rationality to be close to zero if [Gamma] is small enough. This question was first asked, and proved partially, by Serre for families of classical cusp forms of increasing level. In this thesis, we will answer Serre's question affirmatively by converting the question to a question about fields of rationality in families of cuspidal automorphic GL2(A) representations. We will consider the analogous question for certain sequences of open compact subgroups F in UE/F(n). A key intermediate result is an equidistribution theorem for the local components of families of cuspidal automorphic representations.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2016

Author dc:creator

• Binder, John (John Robert)

Advisor dc:contributor.advisor

• Sug Woo Shin.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/104606

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/104606