The algebraic independence of e^θ1,…,e^θs is proved, where θ1,… ,θs are certain gap series or power series of algebraic numbers, or certain transcendental continued fractions with algebraic elements.
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 ≤...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.展开更多
Let ω1,..., ωs be a set of real transcendental numbers satisfying a certain Diophantine inequality. The upper bound for the discrepancy of the Kronecker sequence （{nω1},..., {nωs}）（1 ≤ n ≤ N） is given. In pa...Let ω1,..., ωs be a set of real transcendental numbers satisfying a certain Diophantine inequality. The upper bound for the discrepancy of the Kronecker sequence （{nω1},..., {nωs}）（1 ≤ n ≤ N） is given. In particular, some low-discrepancy sequences are constructed.展开更多
文摘The algebraic independence of e^θ1,…,e^θs is proved, where θ1,… ,θs are certain gap series or power series of algebraic numbers, or certain transcendental continued fractions with algebraic elements.
文摘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.
基金Project supported by National Natural Science Foundation of China(No.10571180)
文摘Let ω1,..., ωs be a set of real transcendental numbers satisfying a certain Diophantine inequality. The upper bound for the discrepancy of the Kronecker sequence （{nω1},..., {nωs}）（1 ≤ n ≤ N） is given. In particular, some low-discrepancy sequences are constructed.
