A Shifted Sum for the Congruent Number Problem
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866915408438624256 |
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| author | Hulse, Thomas A. Kuan, Chan Ieong Lowry-Duda, David Walker, Alexander |
| author_facet | Hulse, Thomas A. Kuan, Chan Ieong Lowry-Duda, David Walker, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1804_02570 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A Shifted Sum for the Congruent Number Problem Hulse, Thomas A. Kuan, Chan Ieong Lowry-Duda, David Walker, Alexander Number Theory 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. |
| title | A Shifted Sum for the Congruent Number Problem |
| topic | Number Theory |
| url | https://arxiv.org/abs/1804.02570 |