Prime Number Error Terms

Speaker: Nathan Ng

Date: Mon, Jun 17, 2024

Location: PIMS, University of British Columbia

Conference: Comparative Prime Number Theory

Subject: Mathematics

Class: Scientific

CRG: L-Functions in Analytic Number Theory


In 1980 Montgomery made a conjecture about the true order of the error term in the prime number theorem. In the early 1990s 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.

Additional Files: