Lethbridge Number Theory and Combinatorics Seminar: Sreerupa Bhattacharjee

This talk will begin with a study on explicit bounds for ψ(x) starting with the work of Rosser in 1941. It will also cover various improvements over the years including the works of Rosser and Schoenfeld, Dusart, Faber-Kadiri, Platt-Trudgian, Büthe, and Fiori-Kadiri-Swidinsky. In the second part of this talk, I will provide an overview of my master's thesis which is a survey on 'Estimating π(x) and Related Functions under Partial RH Assumptions' by Jan Büthe. This article provides the best known bounds for ψ(x) for small values of x in the interval [e50,e3000]. A distinctive feature of this paper is the use of Logan's function and its Fourier Transform. I will be presenting the main theorem in Büthe's paper regarding estimates for ψ(x) with other necessary results required to understand the proof.