Brewer, Sky J (2017) Results in Metric and Analytic Number Theory. PhD thesis, University of York.
Abstract
The following Thesis consists of five chapters. The first three chapters come from Metric Number theory. Chapter 1 discusses algorithms for calculating the
continued fraction of algebraic numbers, as well as presenting experimental results on how well algebraic numbers fit well known conjectures on the distribution of their partial quotients. Chapter 2 discusses
the Singular and Extremality theories of so called ``well separated Dirichlet type systems''. Chapter 3 presents an effective version of the Khintchine-Groshev theorem for simultaneously small linear forms.
The last two chapters are mostly in the area of uniform
distribution. Chapter 4 proves a central limit theorem for the count of the fractional parts of imaginary parts of the zeros of the Riemann zeta function within an interval. Chapter 5 discusses the upper and lower distribution
functions mod $1$ of sequences of the form $(0.a_na_{n+1}a_{n+2} \dots)_{n \in\mathbb N}$, where
the sequence $(a_n)_{n \in \mathbb N}$ has polynomial growth.
Metadata
Supervisors: | Hughes, Christohpher and Velani, Sanju |
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Awarding institution: | University of York |
Academic Units: | The University of York > Mathematics (York) |
Identification Number/EthosID: | uk.bl.ethos.727335 |
Depositing User: | Mr Sky J Brewer |
Date Deposited: | 22 Nov 2017 13:28 |
Last Modified: | 24 Jul 2018 15:23 |
Open Archives Initiative ID (OAI ID): | oai:etheses.whiterose.ac.uk:18381 |
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