Balanced modular parameterizations

Authors

Esteban J. Melendez, University of Texas-Pan American

Date of Award

8-2014

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Timothy Huber

Second Advisor

Dr. Sean Lawton

Third Advisor

Dr. Virgil Pierce

Abstract

In this thesis, we show that Classical representations for certain modular forms have symmetric form. These symmetric formulations are interpreted in terms of more general balanced homogeneous polynomial representations resulting from a permutative action of Hecke congruence subgroups on quotients of theta functions. For prime levels between 5 and 19, sets of permuted theta quotients are constructed that generate the corresponding vector spaces of modular forms of weight one.

Comments

Copyright 2014 Esteban J. Melendez. All Rights Reserved.

https://www.proquest.com/dissertations-theses/balanced-modular-parameterizations/docview/1629825718/se-2

Granting Institution

University of Texas-Pan American