Probabilistic and other methods in multiplicative number theory

近年来，通过引入来自不同领域的思想，特别是概率和组合学，乘法数论取得了一些进展。这篇博士论文将寻求进一步的一些调查，并开发新的。开始，本文期待改善Munsch的一些结果，使几乎尖锐的界限，甚至高时刻的狄利克雷θ函数，从概率数论和其他时刻的问题，以提高和推广Munsch的估计。这是打算，论文将转移到各种其他乘法问题，可能包括丢番图近似或筛选问题。这一切都符合EPSRC的“数论”研究领域。

In recent years there have been several advances in multiplicative number theory by introducing ideas from rather different fields, notably probability and combinatorics. This PhD thesis will seek to further some of these lines of investigation, and develop new ones. To begin, the thesis looks to improve on some results of Munsch giving almost sharp bounds for high even moments of Dirichlet theta functions, introducing ideas from probabilistic number theory and from other moment problems to sharpen and generalise Munsch's estimates. It is intended that the thesis will move on to a variety of other multiplicative questions, possibly including Diophantine approximation or sieve problems. This all fits into EPSRC's "Number theory" research area.