论文标题
整数多项式模型s-Integers的多重依赖轨道上有效界限
Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers
论文作者
论文摘要
我们在代数整数的高度上获得有效界限，该代数整数包含乘法依赖性值模型s-Integer。我们的方法基于在$ \ mathbb {k} $的整数上所谓的多项式值的S-Height上的新上限。我们的结果提供了A.Bérczes，A.Ostafe，I。Shparlinski和J.H.Silverman（Arxiv：1811.04971）对乘法依赖模量有限产生的亚组的有效变体，通过消除K.F.Roth和G.F.F.F.F.F.F.F.F.F.F.F.F.F.F.F.f.f.f.
We obtain effective bounds on the heights of algebraic integers whose orbits contain multiplicatively dependent values modulo S-integers. Our method is based on a new upper bound on the so-called S-height of polynomial values over the ring of integers of $\mathbb{K}$. Our results provide an effective variant of a recent result of A.Bérczes, A.Ostafe, I.E.Shparlinski and J.H.Silverman (arXiv:1811.04971) on multiplicative dependence modulo a finitely generated subgroup by eliminating the use of non-effective results by K.F.Roth and G.Faltings.
