The Bombieri-Vinogradov Theorem (series unlisted)

Abstract: The Siegel-Walfisz theorem gives a main term and error for the number of primes up to $X$ in a given congruence class. The error term is weak, but improves if one assumes the generalized Riemann hypothesis (GRH). If we average over a range of moduli $q \leq Q$, we can improve the Siegel-Walfisz error term to roughly match what one expects from GRH. This major result is the Bombieri-Vinogradov theorem. In this talk, we introduce the Bombieri-Vinogradov theorem and explain how it derives from the large sieve. This is the first lecture in our series on Maynard's recent papers extending the Bombieri-Vinogradov theorem to moduli $q > \sqrt{X}$ (under certain assumptions on $q$).

number theory

Audience: researchers in the topic

London ANT Study Group