ACHIEVEMENTS AND PROBLEMS IN DIOPHANTINE APPROXIMATION THEORY
ACHIEVEMENTS AND PROBLEMS IN DIOPHANTINE APPROXIMATION THEORY
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丢番图近似理论的成就与问题
DOI：
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发表时间：
1980
期刊：
影响因子：
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通讯作者：
V. G. Sprindzhuk
中科院分区：
文献类型：
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作者：
V. G. Sprindzhuk
内容简介 一、流形逼近的度量理论 ??1．基本问题??2．结果简述??3．主要猜想二．超越数度量理论 1．马勒的数字分类 2．具有给定类型近似值的数字的度量特征 ??3．进一步的问题 III．用有理数逼近代数数 ??1．联立近似 ??2．纳入p-adic 指标??3。刘维尔不等式的有效改善 IV．代数数对数线性形式的估计 ??1．基本方法??2．结果调查??3． p-adic 度量中的估计 V. 丢番图方程 ??1．三元指数方程 ??2． Thue 和 Thue-Mahler 方程 ??3．超椭圆型方程 ??4．代数指数方程 VI。多项式的算术结构和类数 1．一个变量中多项式的最大素因数 ??2．两个变量多项式的最大素因数 ??3．多项式的无平方因数和类数4。类数大小的一般问题结论参考文献
ContentsIntroduction I. Metrical theory of approximation on manifolds ??1. The basic problem ??2. Brief survey of results ??3. The principal conjecture II. Metrical theory of transcendental numbers ??1. Mahler's classification of numbers ??2. Metrical characterization of numbers with a given type of approximation ??3. Further problems III. Approximation of algebraic numbers by rationals ??1. Simultaneous approximations ??2. The inclusion of p-adic metrics ??3. Effective improvements of Liouville's inequality IV. Estimates of linear forms in logarithms of algebraic numbers ??1. The basic method ??2. Survey of results ??3. Estimates in the p-adic metric V. Diophantine equations ??1. Ternary exponential equations ??2. The Thue and Thue-Mahler equations ??3. Equations of hyperelliptic type ??4. Algebraic-exponential equations VI. The arithmetic structure of polynomials and the class number ??1. The greatest prime divisor of a polynomial in one variable ??2. The greatest prime divisor of a polynomial in two variables ??3. Square-free divisors of polynomials and the class number ??4. The general problem of the size of the class number Conclusion References