Speaker: Nathan Ng (University of Lethbridge)

Title: Prime number error terms

Abstract: In 1980 Montgomery made a conjecture on the true order of the error term in

the prime number theorem. In the early 1990’s Gonek made an analogous conjecture

for the sum of the Mobius function. In 2012 I further revised Gonek’s conjecture by

providing a precise limiting constant. This was based on work on large deviations

of sums of independent random variables. Similar ideas can be applied to any prime

number error term. In this talk I will speculate about the true order of prime number

error terms. Recently, Lamzouri showed that a version of the Linear Independence

Conjecture implies part of Montgomery’s conjecture. I will show how Lamzouri’s

argument can be extended to any prime number error term. This talk is based on the

preprint https://arxiv.org/abs/2505.11295.