A Shifted Sum for the Congruent Number Problem
Number Theory
2025-07-28 v2
Abstract
We introduce a shifted convolution sum that is parametrized by the squarefree natural number . The asymptotic growth of this series depends explicitly on whether or not 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.
Keywords
Cite
@article{arxiv.1804.02570,
title = {A Shifted Sum for the Congruent Number Problem},
author = {Thomas A. Hulse and Chan Ieong Kuan and David Lowry-Duda and Alexander Walker},
journal= {arXiv preprint arXiv:1804.02570},
year = {2025}
}