Kunjakanan Nath, University of Illinois, Urbana-Champaign
"Circle method and binary correlation problems"
One of the key problems in number theory is to understand the correlation between two arithmetic functions. In general, it is an extremely difficult question and often leads to famous open problems like the Twin Prime Conjecture, the Goldbach Conjecture, and the Chowla Conjecture, to name a few. In this talk, we will discuss a few binary correlation problems involving primes, square-free integers, and integers with restricted digits. The objective is to demonstrate the application of Fourier analysis (aka the circle method) in conjunction with the arithmetic structure of the given sequence and the bilinear form method to solve these problems.
Zoom link: https://uwaterloo.zoom.us/j/98937322498?pwd=a3RpZUhxTkd6LzFXTmcwdTBCMWs0QT09