On a conjecture of Erdős and certain Dirichlet series

Abstract

Let f : ‫ޚ‪/q‬ޚ‬ → ‫ޚ‬ be such that f (a) = ±1 for 1 ≤ a < q, and f (q) = 0. Then Erdős conjectured that n≥1 f (n)/n = 0.For q even, it is easy to show that the conjecture is true.The case q ≡ 3 (mod 4) was solved by Murty and Saradha.In this paper, we show that this conjecture is true for 82% of the remaining integers q ≡ 1 (mod 4).

Locations

• Pacific Journal of Mathematics - View - PDF
• arXiv (Cornell University) - View - PDF