Seminars & Colloquia Calendar
The proof of the Prime Number Theorem in Rudin's Functional Analysis
David Herrera - Rutgers University
Date & time: Tuesday, 13 April 2021 at 4:00PM - 5:00PM
Abstract: You may have seen any of various proofs of PNT. We will explore the proof of PNT in Walter Rudin's Functional Analysis text. We discuss: The standard transformation of PNT into the asymptotics of Chebyshev's psi function, Tauberian theorems in general, How PNT follows from Ingham's Tauberian Theorem, Wiener's Theorem and Wiener's Tauberian theorem, and end with a proof of Ingham's Tauberian theorem (and hence PNT). One should obtain the main ideas going into these results and we will discuss as much of the proofs as we can given time constraints.