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:


Tea or Coffee: Please bring your own.


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.

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