排序方式: 共有69条查询结果,搜索用时 15 毫秒
1.
2.
3.
Artūras Dubickas 《Czechoslovak Mathematical Journal》2006,56(3):949-956
We prove that every cyclic cubic extension E of the field of rational numbers contains algebraic numbers which are Mahler measures but not the Mahler measures of algebraic
numbers lying in E. This extends the result of Schinzel who proved the same statement for every real quadratic field E. A corresponding conjecture is made for an arbitrary non-totally complex field E and some numerical examples are given. We also show that every natural power of a Mahler measure is a Mahler measure. 相似文献
4.
Arturas Dubickas 《Siberian Mathematical Journal》2006,47(5):879-882
Let ξ ≠ = 0 and α > 1 be reals. We prove that the fractional parts {ξ αn}, n = 1, 2, 3, ..., take every value only finitely many times except for the case when α is the root of an integer: α = q 1/d, where q ≥ 2 and d ≥ 1 are integers and ξ is a rational factor of a nonnegative integer power of α. 相似文献
5.
6.
A. Dubickas 《Lithuanian Mathematical Journal》1995,35(4):328-332
We give a lower bound for |α−1|, where α is an algebraic number, and also an upper bound for the number of real zeros of a
polynomial. A lower bound for the maximal modulus of conjugates of a totally real algebraic integer is also obtained.
Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 35, No. 4, pp.
421–431, October–December, 1995. 相似文献
7.
8.
9.
Artūras Dubickas 《Proceedings Mathematical Sciences》2005,115(4):391-397
Suppose that α > 1 is an algebraic number and ξ > 0 is a real number. We prove that the sequence of fractional partsξα
n
, n = 1, 2, 3, …, has infinitely many limit points except when α is a PV-number and ξ ∈ ℚ(α). For ξ = 1 and α being a rational
non-integer number, this result was proved by Vijayaraghavan. 相似文献
10.
Artūras Dubickas 《Archiv der Mathematik》2007,88(1):29-34
Let K be a number field. We prove that the set of Mahler measures M(α), where α runs over every element of K, modulo 1 is everywhere dense in [0, 1], except when
or
, where D is a positive integer. In the proof, we use a certain sequence of shifted Pisot numbers (or complex Pisot numbers) in K and show that the corresponding sequence of their Mahler measures modulo 1 is uniformly distributed in [0, 1].
Received: 24 March 2006 相似文献