Citation
Nastasescu, Maria Monica (2016) Nonvanishing of Lfunctions for GL(n). Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9QN64R2. http://resolver.caltech.edu/CaltechTHESIS:06072016183228371
Abstract
In this thesis I study two different approaches towards proving average results on values of Lfunctions, with an interest toward establishing new results on automorphic Lfunctions, especially concerning the nonvanishing of Lfunctions of degree > 2 at the center of the critical strip (and at other points of the complex plane), and their applications, particularly to padic Lfunctions. In the first problem, I evaluate a twisted average of Lvalues using the approximate functional equation in order to prove a result on the determination of isobaric representations of GL(3, AQ) by certain Lvalues of ppower twists. I also provide an application to the adjoint padic Lfunction of an elliptic curve. More specifically, I show that if E is an elliptic curve over Q with semistable reduction at some fixed prime p, then the adjoint padic Lfunction of E evaluated at any infinite set of integers relatively prime to p completely determines up to a quadratic twist the isogeny class of E.
For the second problem, which is part of a long project, I present some results towards proving an average result for the degree 4 Lfunction on GSp(4)/Q at the center using the relative trace formula. More specifically, I consider a suitable relative trace formula such that the spectral side is an average of central Lvalues of genus 2 holomorphic Siegel eigenforms of weight k and level N twisted by some fixed character. I then work towards computing the corresponding geometric side.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  Lfunction, automorphic forms, relative trace formula  
Degree Grantor:  California Institute of Technology  
Division:  Physics, Mathematics and Astronomy  
Major Option:  Mathematics  
Awards:  Scott Russell Johnson Prize for Excellence as a FirstYear Graduate Student, 2012. Apostol Award for Excellence in Teaching in Mathematics, 2013. Scott Russell Johnson Prize for Excellence in Graduate Studies, 2014. Apostol Award for Excellence in Teaching in Mathematics, 2015. Scott Russell Johnson Graduate Dissertation Prize in Mathematics, 2016.  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  1 June 2016  
Record Number:  CaltechTHESIS:06072016183228371  
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:06072016183228371  
DOI:  10.7907/Z9QN64R2  
Related URLs: 
 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  9855  
Collection:  CaltechTHESIS  
Deposited By:  Maria Nastasescu  
Deposited On:  09 Mar 2017 17:50  
Last Modified:  21 Dec 2017 23:59 
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