Mahler型函数值代数无关性的p-adic度量

本文给出Mahler型函数值代数无关性的p-adic度量.     

Mahler型函数值的代数无关度量

利用初等的结式方法研究满足多项式形式的函数方程组的Mahler型函数的零点估计,给出了满足非线性函数方程组的Mahler型函数在代数点值的代数无关度量.     

Mahler型函数值的代数无关度量

利用初等的结式方法研究满足多项式形式的函数方程组的Mahler型函数的零点估计,给出了满足非线性函数方程组的Mahler型函数在代数点值的代效无关度量．     

Mahler函数值的代数无关性

给出M ah ler型函数值超越次数的下界.     

Mahler型函数值的代数无关度量

In this paper,we give the algebraic independence measures for the values of Mahler type functions in complex number field and p-adic number field,respectively.     

关于Mahler超越小数的无理性度量

本文在一般条件下研究了Mahler超越小数的无理性度量,给出无理性指数的上、下界估计及某些特殊小数的无理性指数的精确值．     

p-adic Transcendence and p-adic Transcendence Measures for the Values of Mahler Type Functions

We prove the p-adic transcendence and p-adic transcendence measures for the values of some Mahler type functions.     

广义Mahler级数值的代数无关性

本文给出一组具有特殊参数的广义Ｍａｈｌｅｒ级数在代数点上值的代数无关性．     

关于超越代数体函数的增长与其亏函数个数的关系

设 f(z)为 n 值的超越代数体函数,如果存在 n+1个整函数φ_i(i=0,1,2,…,n)满足T(r,φ_i)=0{T(r,f)},r→∞且δ(φ_i,f)=1(i=0,1,…,n),则 f(z)的级λ为正整数或无穷且是正规增长的.     

代数体函数涉及重值的Borel点

研究了单位圆内代数体函数涉及重值的Borel点的存在性,利用型函数统一证明了单位圆内无穷级,有限正级和部分零级代数体函数存在涉及重值的Borel点,并对有限正级的代数体函数得到两个必要条件.     

p-adic Measures of Algebraic Independence for the Values of Ramanujan Functions and Klein Modular Functions

In this paper, we give the p-adic measures of algebraic independence for the values of Ramanujan functions and Klein modular functions at algebraic points.     

Algebraic Independence of Certain Generalized Mahler Type Numbers

In this paper the generalized Mahler type number Mh（g;A,T） is defined, and in the case of multiplicatively dependent parameters gi, hi（1 ≤ i ≤ s） the algebraic independence of the numbers Mhi （gi; A, T）（1 ≤ i ≤ s） is proved, where A and T are certain infinite sequences of non-negative integers and of positive integers, respectively. Furthermore, the algebraic independence result on values of a certain function connected with the generalized Mahler type number and its derivatives at algebraic numbers is also given.     

Certain Diophantine Properties of the Mahler Measure

It is proved that a polynomial in several Mahler measures with positive rational coefficients is equal to an integer if and only if all these Mahler measures are integers. An estimate for the distance between a metric Mahler measure and an integer is obtained. Finally, it is proved that the ratio of two distinct Mahler measures of algebraic units is irrational.