Paper
On certain correlations into the divisor problem
Authors
Alexandre Dieguez
Abstract
For a fixed irrational with a prescribed irrationality measure function, we study the correlation , where is the Dirichlet error term in the divisor problem. When has a finite irrationality measure, it is known that decorrelation occurs at a rate expressible in terms of this measure. Strong decorrelation occurs for all positive irrationals, except possibly Liouville numbers. We show that for irrationals with a prescribed irrationality measure function , decorrelation can be quantified in terms of .