Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.681488
Title: Numerical methods applied to trace and explicit formulae
Author: Dwyer, Jo
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2014
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Abstract:
In this thesis, we use numerical methods in conjunction with trace or explicit formula to obtain various number theoretical results. The main results are: the derivation of an explicit version of the trace formula that will enable us to compute the low-lying eigenvalues of the spectrum of all congruence subgroups ┌o(N,X) for non-squarefree level, N, and even Dirichlet character, X; we prove new cases of the Artin Conjecture for S5-Artin Representations; we prove an upper bound for ranks of high-ranked elliptic curves. We also use the numerical method of computing an optimal test-function for explicit formulae to investigate the relationship between the rank and zero-repulsion of L-functions corresponding to elliptic curves
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.681488  DOI: Not available
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