Probabilistic and other methods in multiplicative number theory

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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.