Description

Online Number Theory Seminar

Thursday, 26 October, 3.15 pm

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Venue: https://meet.google.com/zrc-owyg-ukt

Host: Ravi Raghunathan

Speaker: Aditi Savalia

Affiliation: IIT Gandhinagar

Title: Limitations to equidistribution in arithmetic progressions

Abstract: It is well known that prime numbers are equidistributed in arithmetic progressions. Such a phenomenon is also observed more generally for a class of arithmetic functions. A key result in this context is the Bombieri-Vinogradov theorem which establishes that the primes are equidistributed in arithmetic progressions “on average” for moduli $q$ in the range $q ≤ x^{1/2−\epsilon}$ for any $\epsilon > 0$. Building on the idea of Maier, Friedlander and Granville showed that such equidistribution results fail if the range of the moduli $q$ is extended to $q ≤ x/(log x)^B$ for any $B > 1$. We discuss variants of this result and give some applications. This is joint work with Akshaa Vatwani.

Description

Venue: https://meet.google.com/zrc-owyg-ukt

Date

Thu, October 26, 2023

Start Time

3:15pm IST

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Mon, October 23, 2023 10:50am IST