Gauss and p-adic numbers
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914090479255552 |
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| author | Lemmermeyer, Franz |
| author_facet | Lemmermeyer, Franz |
| contents | In his notebooks, Gauss recorded various calculations with "infinite congruences". These infinite congruences are p-adic numbers; Gauss computes a square root of $5$ in the $11$-adic integers in order to find an $11$-adic approximation to a quadratic Gauss sum, computes a nontrivial square root of $1$ in $10$-adic integers, and computes the $10$-adic logarithms of small natural numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gauss and p-adic numbers Lemmermeyer, Franz Number Theory History and Overview 01A55 In his notebooks, Gauss recorded various calculations with "infinite congruences". These infinite congruences are p-adic numbers; Gauss computes a square root of $5$ in the $11$-adic integers in order to find an $11$-adic approximation to a quadratic Gauss sum, computes a nontrivial square root of $1$ in $10$-adic integers, and computes the $10$-adic logarithms of small natural numbers. |
| title | Gauss and p-adic numbers |
| topic | Number Theory History and Overview 01A55 |
| url | https://arxiv.org/abs/2510.11559 |