A shifted sum for the congruent number problem

被引：0
|
作者：
Thomas A. Hulse
Chan Ieong Kuan
David Lowry-Duda
Alexander Walker
机构：
[1] Boston College,Department of Mathematics
[2] Sun Yat-Sen University,School of Mathematics (Zhuhai)
[3] University of Warwick,University of Warwick Mathematics Instititue
[4] Rutgers University,Department of Mathematics
来源：
The Ramanujan Journal | 2020年 / 51卷
关键词：
Congruent number problem; Elliptic curves; Shifted convolution sums; Asymptotics; 11N37; 11G05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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 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.
引用
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页码：267 / 274
页数：7
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