Publication Date

Spring 5-12-2024

Abstract

We discuss herein the history, layout, and philosophy of the Hardy-Littlewood Circle method, as well as the more modern renditions thereof. The limitations and scope of each method presented is discussed in detail, providing examples of cases where the failure of the circle method is of relevance. We include a summary of famous problems which have been resolved using each methodology, as well as what limitations each methodology showcases.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Maria Cristina Pereyra

Second Committee Member

Matthew Blair

Third Committee Member

Maxim Zinchenko

Language

English

Keywords

Number Theory, Analytic Number Theory, Circle Method

Document Type

Thesis

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Included in

Mathematics Commons

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