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Number Theory Seminar

Title: Limitations to equidistribution in arithmetic progressions
Speaker: Akshaa Vatwani (IIT Gandhinagar)
Date: 28 September 2022
Time: 11.30 AM
Venue: LH 1

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.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 17 May 2024