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
CRG: L-Functions in Analytic Number Theory
Date: Wed, Jan 25, 2023
Location: PIMS, University of Lethbridge
Conference: L-Functions in Analytic Number Theory Seminar
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Abstract:
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.