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University of Illinois at Urbana-Champaign
Transformations of Theta-Functions and Analogues of Dedekind Sums
Abstract
dc:descriptionCertain arithmetical sums arise in the transformation formulae for the logarithms of the classical theta-functions. These sums, which we refer to as Berndt sums, are analogous to Dedekind sums, which arise in a similar manner from the transformation formula for the logarithm of the Dedekind eta-function. In this thesis, we deduce a number of properties of these sums, and demonstrate the central role they play in a variety of results concerning the theta-functions.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2014
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Goldberg, Larry A.
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (UMI)AAI8203470
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/68188