An explicit error term in the prime number theorem for large x

Speaker: Daniel Johnston

Date: Wed, Jan 25, 2023

Location: PIMS, University of Lethbridge

Conference: L-Functions in Analytic Number Theory Seminar

Subject: Mathematics, Number Theory

Class: Scientific


In 1896, the prime number theorem was established, showing that π(x) ∼ li(x). Perhaps the most widely used estimates in explicit analytic number theory are bounds on |π(x)-li(x)| or the related error term |θ(x)-x|. In this talk we discuss methods one can use to obtain good bounds on these error terms when x is large. Moreover, we will explore the many ways in which these bounds could be improved in the future.