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

Abstract

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.

arXiv commentPhD thesis defended at the University of Bristol

Cited by in corpus (1)

• On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class