Moments of the distribution of $k$-free numbers in short intervals and arithmetic progressions

Abstract

We show estimates for the distribution of $k$-free numbers in short intervals and arithmetic progressions. We argue that, at least in certain ranges, these estimates agree with a conjecture by H. L. Montgomery.

16 pages, comments are welcome!

References in corpus (1)

• On the variance of squarefree integers in short intervals and arithmetic progressions