Integral Moments of Quadratic Dirichlet L-functions: A Computational Perspective

In recent years, the moments of L-functions has been a topic of growing interest in the field of analytic number theory. New techniques, including applications of Random Matrix Theory and multiple Dirichlet series, have lead to many well-posed theorems and conjectures for the moments of various L-fu...

Full description

Bibliographic Details
Main Author:	Alderson, Matthew
Language:	en
Published:	2010
Subjects:	integral moments quadratic Dirichlet L-functions quadratic Dirichlet characters Dedekind zeta function Pure Mathematics
Online Access:	http://hdl.handle.net/10012/5085

id	ndltd-WATERLOO-oai-uwspace.uwaterloo.ca-10012-5085
record_format	oai_dc
spelling	ndltd-WATERLOO-oai-uwspace.uwaterloo.ca-10012-50852013-01-08T18:53:21ZAlderson, Matthew2010-04-27T18:10:04Z2010-04-27T18:10:04Z2010-04-27T18:10:04Z2010-04-27http://hdl.handle.net/10012/5085In recent years, the moments of L-functions has been a topic of growing interest in the field of analytic number theory. New techniques, including applications of Random Matrix Theory and multiple Dirichlet series, have lead to many well-posed theorems and conjectures for the moments of various L-functions. In this thesis, we theoretically and numerically examine the integral moments of quadratic Dirichlet $L$-functions. In particular, we exhibit and discuss the conjectures for the moments which result from the applications of Random Matrix Theory, number theoretic heuristics, and the theory of multiple Dirichlet series. In the case of the cubic moment, we further numerically investigate the possible existence of additional lower order main terms.enintegral momentsquadratic Dirichlet L-functionsquadratic Dirichlet charactersDedekind zeta functionIntegral Moments of Quadratic Dirichlet L-functions: A Computational PerspectiveThesis or DissertationPure MathematicsMaster of MathematicsPure Mathematics
collection	NDLTD
language	en
sources	NDLTD
topic	integral moments quadratic Dirichlet L-functions quadratic Dirichlet characters Dedekind zeta function Pure Mathematics
spellingShingle	integral moments quadratic Dirichlet L-functions quadratic Dirichlet characters Dedekind zeta function Pure Mathematics Alderson, Matthew Integral Moments of Quadratic Dirichlet L-functions: A Computational Perspective
description	In recent years, the moments of L-functions has been a topic of growing interest in the field of analytic number theory. New techniques, including applications of Random Matrix Theory and multiple Dirichlet series, have lead to many well-posed theorems and conjectures for the moments of various L-functions. In this thesis, we theoretically and numerically examine the integral moments of quadratic Dirichlet $L$-functions. In particular, we exhibit and discuss the conjectures for the moments which result from the applications of Random Matrix Theory, number theoretic heuristics, and the theory of multiple Dirichlet series. In the case of the cubic moment, we further numerically investigate the possible existence of additional lower order main terms.
author	Alderson, Matthew
author_facet	Alderson, Matthew
author_sort	Alderson, Matthew
title	Integral Moments of Quadratic Dirichlet L-functions: A Computational Perspective
title_short	Integral Moments of Quadratic Dirichlet L-functions: A Computational Perspective
title_full	Integral Moments of Quadratic Dirichlet L-functions: A Computational Perspective
title_fullStr	Integral Moments of Quadratic Dirichlet L-functions: A Computational Perspective
title_full_unstemmed	Integral Moments of Quadratic Dirichlet L-functions: A Computational Perspective
title_sort	integral moments of quadratic dirichlet l-functions: a computational perspective
publishDate	2010
url	http://hdl.handle.net/10012/5085
work_keys_str_mv	AT aldersonmatthew integralmomentsofquadraticdirichletlfunctionsacomputationalperspective
_version_	1716573519511289856

Integral Moments of Quadratic Dirichlet L-functions: A Computational Perspective

Similar Items