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dc.contributor.authorDroll, Andrew
dc.contributor.otherQueen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))en
dc.date2012-07-31 13:14:03.414en
dc.date.accessioned2012-08-09T14:07:49Z
dc.date.available2012-08-09T14:07:49Z
dc.date.issued2012-08-09
dc.identifier.urihttp://hdl.handle.net/1974/7352
dc.descriptionThesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2012-07-31 13:14:03.414en
dc.description.abstractIn 1997, Xian-Jin Li gave an equivalence to the classical Riemann hypothesis, now referred to as Li's criterion, in terms of the non-negativity of a particular infinite sequence of real numbers. We formulate the analogue of Li's criterion as an equivalence for the generalized quasi-Riemann hypothesis for functions in an extension of the Selberg class, and give arithmetic formulae for the corresponding Li coefficients in terms of parameters of the function in question. Moreover, we give explicit non-negative bounds for certain sums of special values of polygamma functions, involved in the arithmetic formulae for these Li coefficients, for a wide class of functions. Finally, we discuss an existing result on correspondences between zero-free regions and the non-negativity of the real parts of finitely many Li coefficients. This discussion involves identifying some errors in the original source work which seem to render one of its theorems conjectural. Under an appropriate conjecture, we give a generalization of the result in question to the case of Li coefficients corresponding to the generalized quasi-Riemann hypothesis. We also give a substantial discussion of research on Li's criterion since its inception, and some additional new supplementary results, in the first chapter.en_US
dc.languageenen
dc.language.isoenen_US
dc.relation.ispartofseriesCanadian thesesen
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.subjectSelberg classen_US
dc.subjectLi's criterionen_US
dc.subjectGRHen_US
dc.subjectRHen_US
dc.subjectNumber Theoryen_US
dc.subjectzero-free regionsen_US
dc.subjectarithmetic formulaeen_US
dc.subjectRiemann hypothesisen_US
dc.titleVariations of Li's criterion for an extension of the Selberg classen_US
dc.typethesisen_US
dc.description.degreePh.Den
dc.contributor.supervisorMurty, Maruti Ramen
dc.contributor.departmentMathematics and Statisticsen


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