## Sunday, October 24, 2021

### Akshaa Vatwani (IIT, Gandhinagar) - Thursday October 28, 3:55 PM - 5:00 PM (IST)

Dear all,

The next speaker in our seminar is Akshaa Vatwani of IIT, Gandhinagar

Talk Announcement:

Title: Limitations to equidistribution in arithmetic progressions

Speaker: Akshaa Vatwani (IIT, Gandhinagar)

When: Thursday, October 28, 2021 - 4:00 PM - 5:00 PM (IST)

Where: Zoom:

It is well known that the 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 $q \le x^{1/2 -\epsilon }$ for any $\epsilon>0$. In $1989$, building on an idea of Maier, Friedlander and Granville showed that such equidistribution results fail if the range of the moduli $q$ is extended to $q \le x/ (\log x)^B$  for any $B>1$. We discuss variants of this result and give some applications. This is joint work with Aditi Savalia.