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dc.contributor.authorPathak, Siddhi
dc.contributor.otherQueen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))en
dc.date.accessioned2019-04-30T20:28:18Z
dc.date.available2019-04-30T20:28:18Z
dc.identifier.urihttp://hdl.handle.net/1974/26145
dc.description.abstractThis thesis is centered around the theme of special values of L-functions and other infinite series, which are often expected to be transcendental numbers. More specifically, we focus on the following two questions in various scenarios: a) expressing the values in terms of certain special functions, b) determining their arithmetic nature (i.e., whether they are rational or irrational, algebraic or transcendental). Motivated by the conjectures of S. Chowla and P. Erdos, we first study the L-series L(s,f) attached to a periodic arithmetical function f. Utilizing tools from transcendental number theory, we investigate the non-vanishing and the arithmetic nature of the values L(1,f) and L'(1,f). We introduce a probabilistic viewpoint towards the study of the values L(k,f) for any integer k greater than or equal to 1, especially in the case when f is an Erdos function. On a related note, we explore the irrationality of the values of Dedekind zeta-functions at positive integers using elementary means. We also initiate the study of the sum over lattice points, of a rational function. This opens new doors for future research.en_US
dc.language.isoenen_US
dc.relation.ispartofseriesCanadian thesesen
dc.rightsQueen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canadaen
dc.rightsProQuest PhD and Master's Theses International Dissemination Agreementen
dc.rightsIntellectual Property Guidelines at Queen's Universityen
dc.rightsCopying and Preserving Your Thesisen
dc.rightsThis publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.en
dc.subjectDirichlet seriesen_US
dc.subjectTranscendental number theoryen_US
dc.subjectNon-vanishing of L(1,f)en_US
dc.subjectElliptic functionsen_US
dc.subjectSpecial values of zeta-functionsen_US
dc.titleSpecial values of L-series, periodic coefficients and related themesen_US
dc.typethesisen
dc.description.degreeDoctor of Philosophyen_US
dc.contributor.supervisorMurty, Ram
dc.contributor.departmentMathematics and Statisticsen_US


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