Linear correlations amongst numbers represented by positive definite binary quadratic forms
Number Theory
2012-06-20 v3
Abstract
Given a positive definite binary quadratic form f, let r(n) = |{(x,y): f(x,y)=n}| denote its representation function. In this paper we study linear correlations of these functions. For example, if r_1, ..., r_k are representation functions, we obtain an asymptotic for sum_{n,d} r_1(n) r_2(n+d) ... r_k(n+ (k-1)d).
Keywords
Cite
@article{arxiv.1106.4690,
title = {Linear correlations amongst numbers represented by positive definite binary quadratic forms},
author = {Lilian Matthiesen},
journal= {arXiv preprint arXiv:1106.4690},
year = {2012}
}
Comments
60 pages. Small corrections