A Shifted Sum for the Congruent Number Problem

Abstract

We introduce a shifted convolution sum that is parametrized by the squarefree natural number $t$. The asymptotic growth of this series depends explicitly on whether or not $t$ is a \emph{congruent number}, an integer that is the area of a rational right triangle. This series presents a new avenue of inquiry for The Congruent Number Problem.

Cited by in corpus (2)

• Triple Correlation Sums of Coefficients of Cusp Forms
• Congruent number triangles with the same hypotenuse