Date of Award
8-2014
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Legacy Department
Mathematical Science
Committee Chair/Advisor
Associate Professor Jim Brown
Committee Member
Professor Kevin James
Committee Member
Associate Professor Hui Xue
Committee Member
Assistant Professor Michael Burr
Abstract
In this Dissertation we consider stripping primes from the level of genus 2 cuspidal Siegel eigenforms. Specifically, given an eigenform of level Nlr which satisfies certain mild conditions, where l is a prime not dividing N, we construct an eigenform of level N which is congruent to our original form. To obtain our results, we use explicit constructions of Eisenstein series and theta functions to adapt ideas from a level stripping result on elliptic modular forms. Furthermore, we give applications of this result to Galois representations and provide evidence for an analog of Serre's conjecture in the genus 2 case.
Recommended Citation
Keaton, Rodney, "Level stripping of genus 2 Siegel modular forms" (2014). All Dissertations. 1294.
https://tigerprints.clemson.edu/all_dissertations/1294