On a conjecture of Erdős
Speaker:
Abhishek Bharadwaj
Date and Time:
Wednesday, May 29, 2024 - 3:40pm to 3:55pm
Location:
Fields Institute, Room 230
Abstract:
In a written communication to Livingston, Paul Erdős proposed the following conjecture:
If N is a positive integer and f is an arithmetic function with period N and f(n)∈{−1,1} when n=1,2,…,N−1 and f(n)=0 whenever n≡0mod then \displaystyle \sum \limits_{n \ge 1} \frac{f(n)}{n} \neq 0.
We describe the literature around this conjecture, and mention some new results. This is an ongoing joint work with Ram Murty and Siddhi Pathak.