CMI-IMSc Number Theory Seminar
Date: Tuesday,10 September 2024
Time: 3:30 pm to 4:30 pm
Venue: Seminar Hall, CMI
A conjecture of Erdos on non-vanishing of L(1,F)
Siddhi Pathak
Chennai Mathematical Institute.
10-09-24

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Abstract

Let F be an arithmetic function on integers, periodic with period N, such that F(n) is -1 or 1 when n is not a multiple of N, and 0 otherwise. One can associate a Dirichlet series with F in the natural way by setting L(s,F) = \sum_n F(n) n^(-s). In the 1970s, Erdos conjectured that the value L(1,F) is non-zero, whenever the above series is entire. This question is in the same spirit as the non-vanishing of L(1,\chi) for non-principal Dirichlet characters \chi, which implies the infinitude of primes in arithmetic progression.

In this talk, we discuss a new approach to Erdos's conjecture and present recent results obtained in a joint work with Abhishek Bharadwaj and Ram Murty.