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.