دورية أكاديمية
Sur les équations fonctionelles $p$-adiques aux $q$-différences
| العنوان: | Sur les équations fonctionelles $p$-adiques aux $q$-différences |
|---|---|
| المؤلفون: | Bézivin, J.-P. |
| المصدر: | Collectanea Mathematica; 1992: Vol.: 43 Núm.: 2; p. 125-140 |
| Publication Status: | published |
| بيانات النشر: | Universitat de Barcelona, 1992. |
| سنة النشر: | 1992 |
| الوصف: | In this paper, we study the convergence of formal power series $\Phi$ solutions of functional equations of the form $\sum^t_0 P_i(x)\Phi(\varphi^{[i]}(x))=\\tau(x)$ where the base field is the field $\mathbb{C}_p$ of $p$-adic numbers for a prime number $p$, and $\varphi{[k]}$ denotes the $k$-th iterate of the function $\varphi$. The case when the base field is $\mathbb{C}$ has been studien in a previous paper.\newline As an application, we prove that a formal power series solution of a system of a $q_1$-difference equation and of a $q_2$-difference equation is the Taylor series at the origin of a rational function, when the base field is the field of algebraic numbers and $q_1,q_2$ multiplicatively independents, or for a base field $K$, commutative with zero characteristic and $q_1,q_2$ algebraically independents. |
| نوع الوثيقة: | article |
| وصف الملف: | application/pdf |
| اللغة: | Catalan; Valencian |
| تدمد: | 2038-4815 0010-0757 |
| Relation: | https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56704/66460 |
| URL الوصول: | https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56704 |
| رقم الأكسشن: | edsrac.56704 |
| قاعدة البيانات: | RACO (Revistes Catalanes amb Accés Obert) |
| تدمد: | 20384815 00100757 |
|---|