An explicit estimate on the mean value of the error in the prime number theorem in intervals
Speaker: Michaela Cully-Hugill
Date: Tue, Oct 3, 2023
Location: PIMS, University of Lethbridge, Online
Conference: Analytic Aspects of L-functions and Applications to Number Theory
Subject: Mathematics
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Date: Tue, Oct 3, 2023
Location: PIMS, University of Lethbridge, Online
Conference: Analytic Aspects of L-functions and Applications to Number Theory
Subject: Mathematics
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Abstract:
The prime number theorem (PNT) gives us the density of primes amongst the natural numbers. We can extend this idea to consider whether we have the asymptotic number of primes predicted by the PNT in a given interval. Currently, this has only been proven for sufficiently large intervals. We can also consider whether the PNT holds for sufficiently large intervals ‘on average’. This requires estimating the mean-value of the error in the PNT in intervals. A new explicit estimate for this will be given based on the work of Selberg in 1943, along with two applications: one for primes in intervals, and one for Goldbach numbers in intervals.
