تقرير
Pythagoras numbers of orders in biquadratic fields
| العنوان: | Pythagoras numbers of orders in biquadratic fields |
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| المؤلفون: | Krásenský, Jakub, Raška, Martin, Sgallová, Ester |
| المصدر: | Expo. Math. 40, 1181--1228 (2022) |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11E25 (Primary), 11E12, 11R04, 11R80 (Secondary) |
| الوصف: | We examine the Pythagoras number $\mathcal{P}(\mathcal{O}_K)$ of the ring of integers $\mathcal{O}_K$ in a totally real biquadratic number field $K$. We show that the known upper bound $7$ is attained in a large and natural infinite family of such fields. In contrast, for almost all fields $\mathbb{Q}(\sqrt5, \sqrt{s})$ we prove $\mathcal{P}(\mathcal{O}_K)=5$. Further we show that $5$ is a lower bound for all but seven fields $K$ and $6$ is a lower bound in an asymptotic sense. Comment: 44 pages. A minor correction: By mistake, we originally quoted another paper by M. Peters for the results on real quadratic fields |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.exmath.2022.06.002 |
| URL الوصول: | http://arxiv.org/abs/2105.08860 |
| رقم الأكسشن: | edsarx.2105.08860 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.exmath.2022.06.002 |
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