Distribution Of Square-free Numbers Research Articles

On the distribution of squarefree numbers

We develop estimates for multiple exponential sums, by which we can improve the result of 1993 on the distribution of squarefree numbers (under RH, as usual).

Squarefree numbers in arithmetic progressions

We give asymptotics for correlation sums linked with the distribution of squarefree numbers in arithmetic progressions over a fixed modulus. As a particular case we improve previous results concerning the variance.

The distribution of values of the enumerating function of finite, non-isomorphic abelian groups in short intervals

The result is: The distribution of values of the enumerating function of finite, non-isomorphic abelian groups in short intervals is similar to the distribution of square-free numbers in short intervals. Moreover, a new estimate of the error term in the corresponding asymptotic formula is given, which improves former estimates.

The distribution of squarefree numbers.

The distribution of squarefree numbers.

The distribution of square-free numbers

The distribution of square-free numbers

On the Distribution of Square-Free Numbers

On the Distribution of Square-Free Numbers

The Distribution of Squarefree Numbers

The Distribution of Squarefree Numbers

Experiments concerning the distribution of squarefree numbers

Experiments concerning the distribution of squarefree numbers

On the Distribution of Square-Free Numbers

Erdös [1] has shown that, if the square-free numbers in ascending order be denoted by s1, s2, … , sn, … , then for 0 ≦ γ ≦ 2as x → ∞. In this paper we shall extend this result by proving that the asymptotic formula in fact holds for the wider range 0 ≦ γ ≦ 3.Similar results have been obtained previously by the author in respect of both the sequence of numbers expressible as the sum of two squares and also sequences of numbers relatively prime to given large integers, although the method used here differs from that of the earlier papers [2; 3].