dc.contributor.author Rishikesh dc.date.accessioned 2011-06-17 17:34:30 (GMT) dc.date.available 2011-06-17 17:34:30 (GMT) dc.date.issued 2011-06-17T17:34:30Z dc.date.submitted 2011-06-07 dc.identifier.uri http://hdl.handle.net/10012/6005 dc.description.abstract

Given a positive integer k, Conrey, Farmer, Keating, Rubinstein and Snaith conjectured a formula for the asymptotics of the k-th moments of the central values of quadratic Dirichlet L-functions. The conjectured formula for the moments is expressed as sum of a k(k+1)/2 degree polynomial in log |d|. In the sum, d varies over the set of fundamental discriminants. This polynomial, called the moment polynomial, is given as a k-fold residue. In Part I of this thesis, we derive explicit formulae for first k lower order terms of the moment polynomial.

en

In Part II, we present a formula bounding the average of S(t,f), the remainder term in the formula for the number of zeros of an L-function, L(s,f), where f is a newform of weight k and level N. This is Turing's method applied to cuspforms. We carry out the improvements to Turing's original method including using techniques of Booker and Trudgian. These improvements have application to the numerical verification of the Riemann Hypothesis.

dc.language.iso en en dc.publisher University of Waterloo en dc.subject Mathematics en dc.subject Number Theory en dc.subject Analytic Number Theory en dc.title Lower order terms of moments of L-functions en dc.type Doctoral Thesis en dc.pending false en dc.subject.program Pure Mathematics en uws-etd.degree.department Pure Mathematics en uws-etd.degree Doctor of Philosophy en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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