Quintic polynomials and real cyclotomic fields with large class numbers
Quintic polynomials and real cyclotomic fields with large class numbers
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五次多项式和具有大类数的实分圆域
DOI：
10.1090/s0025-5718-1988-0929552-2
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发表时间：
1988
影响因子：
2
通讯作者：
L. Washington
中科院分区：
文献类型：
--
作者：
R. Schoof;L. Washington
本文研究了Emma Lehmer提出的一类五次多项式。我们证明了根是相应的五次域的基本单位。这些领域有很大的类数和计算的几个例子。结果表明，对于素数p = 641491，p阶分圆域的最大真实的子域的类数可被素数1566401整除。在附录中，我们给出了“最简单的”二次，三次和四次字段的特征。
We study a family of quintic polynomials discoverd by Emma Lehmer. We show that the roots are fundamental units for the corresponding quintic fields. These fields have large class numbers and several examples are calculated. As a consequence, we show that for the prime p = 641491 the class number of the maximal real subfield of the pth cyclotomic field is divisible by the prime 1566401. In an appendix we give a characterization of the "simplest" quadratic, cubic and quartic fields.