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

integral moments;quadratic Dirichlet L-functions;quadratic Dirichlet characters;Dedekind zeta function;Pure Mathematics

Alderson, Matthew

University of Waterloo

关键词: integral moments;    quadratic Dirichlet L-functions;    quadratic Dirichlet characters;    Dedekind zeta function;    Pure Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/5085/1/Alderson_Matthew.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

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 leadto 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, weexhibit 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.