The distribution of kk-tuples of reduced residues

In 1940 Paul Erd\H{o}s made a conjecture about the distribution of reduced residues. Here we study the distribution of $k$-tuple of reduced residues.Comment: To appear in Mathematik

Distribution of squares modulo a composite number

In this paper we study the distribution of squares modulo a square-free number $q$. We also look at inverse questions for the large sieve in the distribution aspect and we make improvements on existing results on the distribution of $s$-tuples of reduced residues.Comment: 22 pages, to appear in IMR