Mathematics Seminar Date: Wednesday, 25 September 2024 Time: 2:00 PM Venue: Seminar Hall A conjecture of Erdos on nonvanishing of L(1,F) Siddhi Pathak Chennai Mathematical Institute. 250924 Abstract Dirichlet's theorem, that there exist infinitely many prime numbers in an arithmetic progression, is one of the fundamental results in number theory. It crucially relies on the fact that the series \sum_n \chi(n) / n is nonzero for all nonprincipal characters \chi, which led Dirichlet to establish the class number formula for quadratic number fields. In a similar spirit, in the 1970s, Erdos considered arithmetic functions F on the integers, periodic with period N > 1 such that F(n) is 1 or +1 when N does not divide n, and 0 otherwise. He conjectured that the series \sum_n F(n)/n should be nonzero, whenever it converges. In this talk, we discuss a new approach to Erdos's conjecture and present recent results obtained in joint work with Abhishek Bharadwaj and Ram Murty.
