On the smallest value of the maximal modulus of an algebraic integer
On the smallest value of the maximal modulus of an algebraic integer
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DOI：
10.1090/s0025-5718-06-01958-2
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发表时间：
2006-12
期刊：
影响因子：
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通讯作者：
G. Rhin;Qiang Wu
中科院分区：
文献类型：
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作者：
G. Rhin;Qiang Wu
一个d次代数整数的房子是它共轭的最大模。对于次数为d的d1，记为m（d）。作为结果，我们改进了Matveev关于m（d）下界的定理.我们表明，在这个范围内，Schinzel-Zassenhaus猜想是满意的。任何代数整数α的最小多项式的房子等于m（d）是一个因子的二，三或四项。计算使用一族显式辅助函数。这些函数依赖于C中某些紧集的整数超限直径的推广。对于小房子代数整数α的极小多项式的系数，它们给出了比经典结果更好的界.
The house of an algebraic integer of degree d is the largest modulus of its conjugates. For d 1 of degree d, say m(d). As a consequence we improve Matveev's theorem on the lower bound of m(d). We show that, in this range, the conjecture of SchinzelZassenhaus is satisfied. The minimal polynomial of any algebraic integer α whose house is equal to m(d) is a factor of a bi-, tri- or quadrinomial. The computations use a family of explicit auxiliary functions. These functions depend on generalizations of the integer transfinite diameter of some compact sets in C. They give better bounds than the classical ones for the coefficients of the minimal polynomial of an algebraic integer α whose house is small.