Statistics of the zeros of $L$-functions and arithmetic correlations

12 Jul 2016 · Smith D. J. ·

This thesis determines some of the implications of non-universal and emergent universal statistics on arithmetic correlations and fluctuations of arithmetic functions, in particular correlations amongst prime numbers and the variance of the expected number of prime numbers over short intervals are generalised by associating these concepts to $L$-functions arising from number theoretic objects.