Citation
Walji, Nahid (2011) Supersingular distribution, congruence class bias, and a refinement of strong multiplicity one. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:02132011055211033
Abstract
This thesis consists of four chapters, including an introduction.
In Chapter 2, we take an averaging approach to the question of the distribution of supersingular primes of degree one, for elliptic curves over a number field. We begin by modifying the LangTrotter heuristic to address the case of an abelian extension, then we show that it holds on average (up to a constant) for a family of elliptic curves by using ideas of DavidPappalardi.
In Chapter 3, we prove constructively that there exists an infinite number of (arbitrarily) thin families of rational elliptic curves for which the LangTrotter conjecture holds on average, in part by using techniques of FouvryMurty.
In Chapter 4, we obtain a result related to the strong multiplicity one theorem for nondihedral cuspidal automorphic representations for GL(2), with trivial central character and nontwistequivalent symmetric squares. Given a real algebraic number, we also find a lower bound for the lower density of the set of finite places for which the associated Hecke eigenvalue is not equal to that algebraic number.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  supersingular distribution, LangTrotter conjecture, strong multiplicity one. 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  6 January 2011 
Record Number:  CaltechTHESIS:02132011055211033 
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:02132011055211033 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  6242 
Collection:  CaltechTHESIS 
Deposited By:  Nahid Walji 
Deposited On:  29 Mar 2011 16:35 
Last Modified:  16 Apr 2013 23:33 
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