Hensel's lemma for general continuous functions

The intermediate value theorem over a non-Archimedean field via Hensel's Lemma

The paper proves that all power series over a maximal ordered Cauchy complete non-Archimedean field satisfy the intermediate value theorem on every closed interval. Hensel's Lemma for restricted power series is the main tool of the proof.

超度量域的多变量亨泽尔引理

Multivariate Hensel Lemma for ultrametric fields

本文在构造性数学框架下，不依赖扎里斯基主定理的格罗滕迪克版本，直接证明了超度量域的多变量亨泽尔引理，并在经典数学中蕴含秩一赋值域情形。

Maps on ultrametric spaces, Hensel's Lemma, and differential equations over valued fields

We give a criterion for maps on ultrametric spaces to be surjective and to preserve spherical completeness. We show how Hensel's Lemma and the multi-dimensional Hensel's Lemma follow from our result. We give an easy proof that the latter holds in every henselian field. We also prove a basic infinite-dimensional Implicit Function Theorem. Further, we apply the criterion to deduce various versions of Hensel's Lemma for polynomials in several additive operators, and to give a criterion for the existence of integration and solutions of certain differential equations on spherically complete valued …

A resultant for Hensel's Lemma

Let R be a complete discrete valuation ring with maximal ideal generated by pi. Let f(X) in R[X] be a monic polynomial with nonzero discriminant Delta(f). Let s >= v_pi(Delta(f)) + 1. Suppose given a factorisation of f(X) in (R/pi^s R)[X] into several factors, not necessarily coprime in (R/pi R)[X]. We lift it uniquely to a factorisation of f(X) in R[X]. This generalises the Hensel-Rychlik Lemma, which covers the case of two factors. We work directly with lifts of factorisations into several factors and avoid having to iterate factorisations into two factors. For this purpose we define a resul…

论有效Pourchet定理

On the effective Pourchet's Theorem

本研究借助Hensel引理改进ISSAC 2023提出的2进Newton多边形算法，实现有效Pourchet定理的计算并扩展适用输入范围，还给出了原有猜想算法无法处理的算例。