تقرير
p-adically convergent loci in varieties arising from periodic continued fractions
| العنوان: | p-adically convergent loci in varieties arising from periodic continued fractions |
|---|---|
| المؤلفون: | Capuano, Laura, Mula, Marzio, Terracini, Lea, Veneziano, Francesco |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11J70, 11D88, !!Y65, 11D09 |
| الوصف: | Inspired by several alternative definitions of continued fraction expansions for elements in $\mathbb Q_p$, we study $p$-adically convergent periodic continued fractions with partial quotients in $\mathbb Z[1/p]$. To this end, following a previous work by Brock, Elkies, and Jordan, we consider certain algebraic varieties whose points represent formal periodic continued fractions with period and preperiod of fixed lengths, satisfying a given quadratic equation. We then focus on the $p$-adically convergent loci of these varieties, characterizing the zero and one-dimensional cases. Comment: 19 pages, comments are welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.00739 |
| رقم الأكسشن: | edsarx.2402.00739 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |