p-adic congruences in iterated derivatives of the Weierstrass elliptic function
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910995551617024 |
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| author | Luecke, Kiran Peterson, Eric |
| author_facet | Luecke, Kiran Peterson, Eric |
| contents | We use homotopy theoretic methods to prove congruence relations of number theoretic interest. Specifically, we use the theory of $\mathbb E_\infty$ complex orientations to establish $p$-adic Kümmer congruences among iterated derivatives of the Weierstrass elliptic function.
The machinery of Ando, Hopkins, and Rezk was developed with the intended application of taking congruence relations as input and producing $\mathbb E_\infty$-orientations as output. We run their machine in reverse, using as input the recent results of Carmeli and the first author on the existence of $\mathbb E_\infty$-orientations of Tate fixed-point objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07420 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | p-adic congruences in iterated derivatives of the Weierstrass elliptic function Luecke, Kiran Peterson, Eric Number Theory Algebraic Topology 55N22, 55S25, 11F33, 11F50 We use homotopy theoretic methods to prove congruence relations of number theoretic interest. Specifically, we use the theory of $\mathbb E_\infty$ complex orientations to establish $p$-adic Kümmer congruences among iterated derivatives of the Weierstrass elliptic function. The machinery of Ando, Hopkins, and Rezk was developed with the intended application of taking congruence relations as input and producing $\mathbb E_\infty$-orientations as output. We run their machine in reverse, using as input the recent results of Carmeli and the first author on the existence of $\mathbb E_\infty$-orientations of Tate fixed-point objects. |
| title | p-adic congruences in iterated derivatives of the Weierstrass elliptic function |
| topic | Number Theory Algebraic Topology 55N22, 55S25, 11F33, 11F50 |
| url | https://arxiv.org/abs/2506.07420 |