Statistics of $K$-groups modulo $p$ for the ring of integers of a varying quadratic number field
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2017
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| _version_ | 1866914000042721280 |
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| author | Jordan, Bruce W. Klagsbrun, Zev Poonen, Bjorn Skinner, Christopher Zaytman, Yevgeny |
| author_facet | Jordan, Bruce W. Klagsbrun, Zev Poonen, Bjorn Skinner, Christopher Zaytman, Yevgeny |
| contents | For each odd prime $p$, we conjecture the distribution of the $p$-torsion subgroup of $K_{2n}(\mathcal{O}_F)$ as $F$ ranges over real quadratic fields, or over imaginary quadratic fields. We then prove that the average size of the $3$-torsion subgroup of $K_{2n}(\mathcal{O}_F)$ is as predicted by this conjecture. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1703_00108 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Statistics of $K$-groups modulo $p$ for the ring of integers of a varying quadratic number field Jordan, Bruce W. Klagsbrun, Zev Poonen, Bjorn Skinner, Christopher Zaytman, Yevgeny Number Theory 11R70 (Primary) 11R29, 19D50, 19F99 (Secondary) For each odd prime $p$, we conjecture the distribution of the $p$-torsion subgroup of $K_{2n}(\mathcal{O}_F)$ as $F$ ranges over real quadratic fields, or over imaginary quadratic fields. We then prove that the average size of the $3$-torsion subgroup of $K_{2n}(\mathcal{O}_F)$ is as predicted by this conjecture. |
| title | Statistics of $K$-groups modulo $p$ for the ring of integers of a varying quadratic number field |
| topic | Number Theory 11R70 (Primary) 11R29, 19D50, 19F99 (Secondary) |
| url | https://arxiv.org/abs/1703.00108 |