The probability that two random integers are coprime

  title={The probability that two random integers are coprime},
  author={Julien Bureaux and Nathanael Enriquez},
  journal={Mathematische Nachrichten},
  pages={24 - 27}
An equivalence is proven between the Riemann hypothesis and the speed of convergence to 6/π2 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. 
1 Citations

Divisibility properties of random samples of integers

This paper is devoted to survey the rich theory, some of it quite recent, concerning the divisibility properties, of various kinds, of random r-tuples of positive integers.



The Theory of the Riemann Zeta-Function

The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects

Fluctuations in the mean of Euler’s phi function

We consider the error term in the mean value estimate of Euler’s phi function ψ(n), and show that it is Ω+- (x(log log x)1/2). This improves on the earlier results of Pillai and Chowla, and of Erdös

An Introduction to the Theory of Numbers

  • E. T.
  • Mathematics
  • 1946
THIS book must be welcomed most warmly into X the select class of Oxford books on pure mathematics which have reached a second edition. It obviously appeals to a large class of mathematical readers.

Smoothing arithmetic error terms: the case of the Euler φ function

In many cases known methods of detecting oscillations of arithmetic error terms involve certain smoothing pro‐cedures. Usually an application of the smoothing operator does not change significantly

Weylsche Exponentialsummen in der neueren Zahlentheorie

Ueber einige asymptotische Gesetze der Zahlentheorie.

JLJen Gegenstand der folgenden Abhandlung bildet eine Reihe von Aufgaben, welche die bei gewissen zahlentheoretischen Functionen in Betracht kommenden asyniptotischen Ausdr cke betreffen. Die zwei

How to cite this article: Bureaux J, Enriquez N. The probability that two random integers are coprime

  • Weylsche Exponentialsummen in der neueren Zahlentheorie, VEB Deutscher Verlag der Wissenschaften
  • 1963