The probability that two random integers are coprime

Abstract

An equivalence is proven between the Riemann hypothesis and the speed of convergence to 6∕ 2 of the probability that two independent random variables following the same geometric distribution are coprime integers, when the parameter of the distribution goes to 0. K E Y W O R D SArithmetic error terms, Euler totient function, Riemann hypothesis M S C ( 2 0 1 0 ) 11N37, 11M26