Variance of sums of arithmetic functions over primes in short intervals

Special Analysis/Number Theory Seminar
Topic:Variance of sums of arithmetic functions over primes in short intervals
Speaker:Jon Keating
Affiliation:University of Bristol
Date:Monday, February 8
Time/Room:4:30pm - 5:30pm/S-101
Video Link:https://video.ias.edu/SANT/2016/0208-Keating

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 pair-correlation conjecture and the Hardy-Littlewood conjecture. I will discuss the generalisation of these formulae to other arithmetic functions associated with the Selberg class of L-functions, in the context of both zero statistics and arithmetic correlations. I also hope to discuss the function-field analogues of these generalisations.