论文标题
关于$ k $ - 估值序列和最后一个非零数字
On $k$-regularity of sequences of valuations and last nonzero digits
论文作者
论文摘要
令$ b \ geq 2 $为一个整数基础，具有主要因素$ p_1，\ ldots，p_s $。在本文中，我们研究了$ b $ b $ ad的序列$ f（n）=（f_1（n），\ ldots，f_s（n））的序列，其中每个$ f_i $ is $ p_i $ p_i $ addic $ addic分析函数。我们给出了有关这些序列的$ K $ regumentity的完整分类，该序列概括了Shu和Yao获得的$ B $ prime的结果。作为应用程序，我们对Murru和Sanna的定理加强了第一类Lucas序列的$ B $ ADIC估值。此外，我们得出了一种精确确定这些序列的术语可以用某些三元二次形式表示的方法。
Let $b \geq 2$ be an integer base with prime factors $p_1, \ldots, p_s$. In this paper we study sequences of "$b$-adic valuations" and last nonzero digits in $b$-adic expansions of the values $f(n) = (f_1(n), \ldots, f_s(n))$, where each $f_i$ is a $p_i$-adic analytic function. We give a complete classification concerning $k$-regularity of these sequences, which generalizes a result for $b$ prime obtained by Shu and Yao. As an application, we strengthen a theorem by Murru and Sanna on $b$-adic valuations of Lucas sequences of the first kind. Moreover, we derive a method to determine precisely which terms of these sequences can be represented by certain ternary quadratic forms.
