Arithmetic Progressions of Squares and Multiple Dirichlet Series

Abstract

We study a Dirichlet series in two variables which counts primitive three-term arithmetic progressions of squares. We show that this multiple Dirichlet series has meromorphic continuation to ${\mathbb{C}}^2$ and use Tauberian methods to obtain counts for arithmetic progressions of squares and rational points on $x^2+y^2=2$.

32 pages, now revised with referee comments

References in corpus (1)

• Triple Correlation Sums of Coefficients of Cusp Forms