Hypergeometric functions and Mahler measure
department or school: Science, Faculty of
department or school: Mathematics, Department of
data provider: DSpace
degree campus: UBCV
creator: Rogers, Mathew D.
issued: 2008-08-20T14:16:15Z
issued: 2008
related degree: Doctor of Philosophy - PhD
degree grantor: University of British Columbia
description: The logarithmic Mahler measure of an n-variable Laurent polynomial, P(x1,...,xn) is defined by [expression]. Using experimental methods, David Boyd conjectured a large number of explicit relations between Mahler measures of polynomials and special values of different types of L-series. This thesis contains four papers which either prove or attempt to prove conjectures due to Boyd. The introductory chapter contains an overview of the contents of each manuscript.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/1420
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format: application/pdf
note: Hypergeometric functions and MahlermeasurebyMathew D. RogersB.Sc., The University of California at Irvine, 2002M.Sc., The University of British Columbia, 2004A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinThe Faculty of Graduate Studies(Mathematics)The University Of British ColumbiaAugust, 2008c© Mathew D. Rogers 2008AbstractThe (logarithmic) Mahler measure of an n-variable Laurent polynomial,P (x1, . . . , xn), is defined bym (P ) =∫ 10. . .∫ 10log∣∣P (e2πit1 , . . . , e2πitn)∣∣ dt1 . . .dtn.Using experimental methods, David Boyd conjectured a large number ofexplicit relations between Mahler measures of polynomials and special val-ues of different types of L-series. This thesis contains four papers whicheither prove or attempt to prove conjectures due to Boyd. The introductorychapter contains an overview of the contents of each manuscript.iiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . viDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiStatement of Co-Authorship . . . . . . . . . . . . . . . . . . . . . viii1 Introductory Chapter . . . . . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Mahler measure background . . . . . . . . . . . . . . . . . . 21.3 An overview of the manuscripts in this thesis . . . . . . . . . 3Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Lattice sums and Mahler measures . . . . . . . . . . . . . . . 102.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.1 Boyd’s conjectures and four-dimensional lattice sums 122.1.2 Summary of hypergeometric formulas for F (b, c) . . . 152.2 Reductions of F (1, 1), F (1, 2), F (1, 4), and F (2, 2) to inte-grals of hype…
has type: Thesis/Dissertation
date issued: 2008-11
is shown at: 10.14288/1.0066504
language: eng
degree discipline: Mathematics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
type: Text
identifier URI: http://hdl.handle.net/2429/1420