标题： 通过有效庞加莱-佩龙方法对代数数的位移对数的近似度量 显示英文标题

标题： Approximation measures for shifted logarithms of algebraic numbers via effective Poincare-Perron

摘要： 在本文中，我们展示了针对属于任意次数数域的代数数的移位对数的新有效逼近度量。我们的度量改进了之前的度量，包括常规对数的度量。我们借鉴了M. Kawashima和A. Poels在有理数情况下构造的Pade逼近。我们的关键工具依赖于Poincare-Perron定理，该定理为我们提供了数域每个阿基米德位置的渐近估计，我们将其应用于判断移位对数是否位于数域之外。我们使用Perron的第二个定理及其由于M. Pituk的修改来处理一般情况。 显示英文摘要

摘要： In this article, we show new effective approximation measures for the shifted logarithm of algebraic numbers which belong to a number field of arbitrary degree. Our measures refine previous ones including those for usual logarithms. We adapt Pade approximants constructed by M. Kawashima and A. Poels in the rational case. Our key ingredient relies on the Poincare-Perron theorem which gives us asymptotic estimates at every archimedean place of the number field, that we apply to decide whether the shifted logarithm lies outside of the number field. We use Perron's second theorem and its modification due to M. Pituk to handle general cases.