Moments and zeros of L-functions

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dc.contributor.authorShen, Quanli
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorKadiri, Habiba
dc.contributor.supervisorNg, Nathan
dc.date.accessioned2021-12-06T21:33:50Z
dc.date.available2021-12-06T21:33:50Z
dc.date.issued2021
dc.degree.levelPh.Den_US
dc.description.abstractWe study moments and zeros of L-functions in this thesis. In Chapter 2, by following closely Soundararajan-Young's method, we prove an asymptotic for the fourth moment of quadratic Dirichlet L-functions under the generalized Riemann hypothesis. Unconditionally, we are able to give a sharp lower bound that agrees with Keating-Snaith's conjecture. In Chapter 3, we use a recursive method that was pioneered by Heath-Brown and developed by Young to give an asymptotic with an error O(X1/2+E) for the smoothed first moment of quadratic twists of modular L-functions. The result is analogous to Sono's work on the second moment of quadratic Dirichlet L-functions. It improves previous results of Iwaniec and Soundararajan-Radziwill. In Chapter 4, we obtain an explicit result for the number of zeros, in a box, of Dedekind zeta functions, which improves a result of Trudgian. Our argument is based on previous works of Bennett-Martin-O'Bryant-Rechnitzer, Kadiri-Ng and Trudgian.en_US
dc.identifier.urihttps://hdl.handle.net/10133/6103
dc.language.isoen_USen_US
dc.proquest.subject0280en_US
dc.proquest.subject0405en_US
dc.proquestyesYesen_US
dc.publisherLethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Scienceen_US
dc.publisher.departmentDepartment of Mathematics & Computer Scienceen_US
dc.publisher.facultyArts and Scienceen_US
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)en_US
dc.subjectmoments of L-functionsen_US
dc.subjectzeros of L-functionsen_US
dc.subjectNumber theoryen_US
dc.subjectL-functionsen_US
dc.subjectDissertations, Academicen_US
dc.titleMoments and zeros of L-functionsen_US
dc.typeThesisen_US
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