Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Number Theory Seminar


Wednesday, November 1st, 2017

Time: 3:30 p.m.  Place: Jeffery Hall 319

Speaker: Siddhi Pathak

Title: On a conjecture of Erdos

Abstract: In a written correspondence with A. Livingston in the 1960s, Erdos conjectured that for an arithmetic function f, periodic with period q satisfying: (i) f(n) is 1 or -1 if q does not divide n and (ii) f(n) = 0 if q divides n, the series \sum_{n=1}^{\infty} f(n)/n is not zero (and hence, evaluates to a transcendental number) whenever it converges. In 2007, this conjecture was proved by M. Ram Murty and N. Saradha for q congruent to 3 modulo 4 and is still open when q is congruent to 1 modulo 4. In this talk, we present some new developments toward this conjecture.