On Cubic Multisections

Authors

Andrew Alaniz, University of Texas-Pan American

Date of Award

8-2013

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Tim Huber

Second Advisor

Dr. Sean Lawton

Third Advisor

Dr. Eleftherios Gkioulekas

Abstract

In this thesis, a systematic procedure is given for generating cubic multi-sections of Eisenstein series. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three. The resulting series are shown to be rational functions of the Dedekind eta function. A more general treatment of cubic dissection formulas is given by describing the dissection operators in terms of linear transformations.

Comments

Copyright 2013 Andrew Alaniz. All Rights Reserved.

https://www.proquest.com/dissertations-theses/on-cubic-multisections/docview/1459462118/se-2

Granting Institution

University of Texas-Pan American