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Sums of Reciprocals and the Three Distance Theorem

Leong, Nicol (2017) Sums of Reciprocals and the Three Distance Theorem. MSc by research thesis, University of York.

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Abstract

This thesis is primarily concerned with sums of reciprocals in number theory. We first give a brief background and introduction to metric number theory, in particular the areas of Diophantine approximation and continued fractions. We then review sums of reciprocals and their significance and usefulness in certain fields of mathematics as a motivation for their study. The Three Distance theorem, also known as the Steinhaus conjecture, is then discussed and we use it to develop a new technique for obtaining bounds for sums of reciprocals, making constants explicit.

Item Type: Thesis (MSc by research)
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Keywords: Steinhaus conjecture, Three gap theorem, Three distance theorem, Sums of reciprocals of fractional parts
Academic Units: The University of York > Mathematics (York)
Depositing User: Mr Nicol Leong
Date Deposited: 26 May 2017 08:16
Last Modified: 26 May 2017 08:16
URI: http://etheses.whiterose.ac.uk/id/eprint/17431

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