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arXiv · 1804.02570

A Shifted Sum for the Congruent Number Problem

Thomas A. Hulse·Chan Ieong Kuan·David Lowry-Duda·Alexander Walker
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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.

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Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda, Alexander Walker. 2018-04-07. A Shifted Sum for the Congruent Number Problem. https://doi.org/10.1007/s11139-018-0131-7

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