Resource type

Thesis type

(Thesis) M.Sc.

Date created

2012-04-12

Authors/Contributors

Author: Ratcliffe, James Wells

Abstract

Given a rational function φ(X) with rational coefficients that is defined at every positive integer, we consider the sum of φ(n) as n runs from 0 to infinity. It is believed that when this sum converges, it converges to either a rational or transcendental number. We prove an analogue of this conjecture over fields of rational functions: Let K be a field and let φ(X) be a rational function with coefficients in K such that φ(0) = 0. Given a positive integer d ≥ 2, we define F(X) to be the sum of φ(X^(d^n)) as n runs from 0 to infinity. If d is not a power of char(K), then F(X) is either a rational function or transcendental over K(X). Our demonstration uses results from the theory of automatic sequences and from commutative algebra.

Document

Identifier

etd7229

Copyright statement

Copyright is held by the author.

Scholarly level

Supervisor or Senior Supervisor

Thesis advisor: Bell, Jason

Member of collection

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etd7229_JRatcliffe.pdf | 982.92 KB |