Show simple item record

dc.contributor.authorWong, Peng-Jieen
dc.date.accessioned2017-08-21T22:56:53Z
dc.date.available2017-08-21T22:56:53Z
dc.identifier.urihttp://hdl.handle.net/1974/22028
dc.description.abstractIn the spirit of Artin, Brauer, and Heilbronn, we implement representation theory together with the Artin formalism to study L-functions in this thesis. One of the major themes is motivated by the work of Heilbronn and many others on classical Heilbronn characters. We define the arithmetic Heilbronn characters and apply them to study L-functions. In particular, we prove a theorem concerning the analytic ranks of elliptic curves as predicted by the Birch-Swinnerton-Dyer conjecture. In a different vein, we employ the theory of supercharacters introduced by Diaconis and Isaacs to derive a supercharacter-theoretic analogue of Heilbronn characters. Moreover, we generalise the effective Chebotarev density theorem due to M. R. Murty, V. K. Murty, and Saradha in the context of supercharacter theory. Lastly, we study the conjectures of Artin and Langlands via group theory and extend the previous work of Arthur and Clozel. For instance, we introduce the notion of near supersolvability and near nilpotency, and show that Artin's conjecture holds if $\Gal(K/k)$ is nearly supersolvable. As a consequence, the Artin conjecture is true for any solvable Frobenius Galois extension. Also, we derive the automorphy for every nearly nilpotent group. Furthermore, the Langlands reciprocity conjecture has been established for Galois extensions of number fields of either square-free degree or odd cube-free degree as well as all non-$A_5$ extensions of degree at most 100.en
dc.language.isoengen
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.rightsCC0 1.0 Universalen
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/
dc.subjectArtin L-functionsen
dc.subjectArtin's conjectureen
dc.subjectAutomorphic representationsen
dc.subjectHeilbronn charactersen
dc.subjectLanglands reciprocity conjectureen
dc.titleCharacter Theory and Artin L-functionsen
dc.typethesisen
dc.description.degreePhDen
dc.contributor.supervisorMurty, M. Ramen
dc.contributor.departmentMathematics and Statisticsen
dc.degree.grantorQueen's University at Kingstonen


Files in this item

Thumbnail
Thumbnail

This item appears in the following Collection(s)

Show simple item record

Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
Except where otherwise noted, this item's license is described as Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada