variance of sums of arithmetic functions over primes in short intervals
variance of sums of arithmetic functions over primes in short intervals

J.Keating , University of Bristol
IAS Room S101
This is a special Analysis/PrincetonIAS Number Theory seminar. Goldston & Montgomery and Montgomery & Soundararajan have established formulae for the variance of sums of the von Magoldt function over short intervals (i.e. for the variance of the number of primes in these intervals) assuming, respectively, the paircorrelation conjecture and the HardyLittlewood conjecture. I will discuss the generalisation of these formulae to other arithmetic functions associated with the Selberg class of Lfunctions, in the context of both zero statistics and arithmetic correlations. I also hope to discuss the functionfield analogues of these generalisations.