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Dedekind sums

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posted on 29.03.2022, 00:41 by Simon Macourt
Dedekind sums arose out of the study of elliptic functions and modular forms. They were iniially discovered by Dedekind but have since been studied for their many arithmetic properties. Much work has been done on Dedekind sums and in 1972 Rademacher and Grosswald released a book that summarised much of what was known, as well as providing a history of Dedekind sums. This encouraged greater interest in this topic and provided groundwork for further research. In our essay we seek to update Rademacher and Grosswald's book by providing an overview of some of the research that has been done since its publication. We will also extend some results of Myerson and Phillips, regarding fixed points of Dedekind sums. It is our intention that our findings will provide a foundation for future research in the study of Dedekind sums.

History

Table of Contents

1. Introduction -- 2. Elementary properties -- 3. The distribution of Dedekind sums -- 4. Related sums, applications and other properties of Dedekind sums -- 5. New results -- 6. Conclusion.

Notes

Theoretical thesis. Bibliography: pages [47]-50

Awarding Institution

Macquarie University

Degree Type

Thesis MRes

Degree

MRes, Macquarie University, Faculty of Science and Engineering, Department of Mathematics

Department, Centre or School

Department of Mathematics

Year of Award

2015

Principal Supervisor

Gerry Myerson

Rights

Copyright Simon Macourt 2015. Copyright disclaimer: http://www.copyright.mq.edu.au

Language

English

Extent

1 online resource (viii, 50 pages)

Former Identifiers

mq:44910 http://hdl.handle.net/1959.14/1073160

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