تقرير
Real quadratic fields with a universal form of given rank have density zero
| العنوان: | Real quadratic fields with a universal form of given rank have density zero |
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| المؤلفون: | Kala, Vítězslav, Yatsyna, Pavlo, Żmija, Błażej |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11A55, 11E12, 11E20, 11H55, 11R11, 11R80 |
| الوصف: | We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadratic form of a given rank, thus establishing a density zero statement. More generally, we obtain such a result for totally positive definite quadratic lattices that represent all the multiples of a given rational integer. Our main tools are short vectors in quadratic lattices combined with an estimate for the number of periodic continued fractions with bounded coefficients. Comment: 18 pages, minor changes |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2302.12080 |
| رقم الأكسشن: | edsarx.2302.12080 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |