Arithmetic Progressions of Squares and Multiple Dirichlet Series
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866909704074035200 |
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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 study a Dirichlet series in two variables which counts primitive three-term arithmetic progressions of squares. We show that this multiple Dirichlet series has meromorphic continuation to $\mathbb{C}^2$ and use Tauberian methods to obtain counts for arithmetic progressions of squares and rational points on $x^2+y^2=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_14324 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Arithmetic Progressions of Squares and Multiple Dirichlet Series Hulse, Thomas A. Kuan, Chan Ieong Lowry-Duda, David Walker, Alexander Number Theory 11N37 (Primary), 11F30 (Secondary) We study a Dirichlet series in two variables which counts primitive three-term arithmetic progressions of squares. We show that this multiple Dirichlet series has meromorphic continuation to $\mathbb{C}^2$ and use Tauberian methods to obtain counts for arithmetic progressions of squares and rational points on $x^2+y^2=2$. |
| title | Arithmetic Progressions of Squares and Multiple Dirichlet Series |
| topic | Number Theory 11N37 (Primary), 11F30 (Secondary) |
| url | https://arxiv.org/abs/2007.14324 |