تقرير
Heights and transcendence of $p$--adic continued fractions
| العنوان: | Heights and transcendence of $p$--adic continued fractions |
|---|---|
| المؤلفون: | Longhi, Ignazio, Murru, Nadir, Saettone, Francesco Maria |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11J70, 11J87 |
| الوصف: | Special kinds of continued fractions have been proved to converge to transcendental real numbers by means of the celebrated Subspace Theorem. In this paper we study the analogous $p$--adic problem. More specifically, we deal with Browkin $p$--adic continued fractions. First we give some new remarks about the Browkin algorithm in terms of a $p$--adic Euclidean algorithm. Then, we focus on the heights of some $p$--adic numbers having a periodic $p$--adic continued fraction expansion and we obtain some upper bounds. Finally, we exploit these results, together with $p$--adic Roth-like results, in order to prove the transcendence of two families of $p$--adic continued fractions. Comment: 13 pages, correction of minor mistakes in the previous version |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2302.04017Test |
| رقم الانضمام: | edsarx.2302.04017 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |