Class Numbers of Orders in Cubic Fields
Class Numbers of Orders in Cubic Fields
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三次域中阶数的类别数
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
A. Deitmar
中科院分区：
文献类型：
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作者：
A. Deitmar
摘要本文证明了复三次域上的阶类数的和服从一个与素数相似的渐近规律，即当调节器的界趋于无穷时。这里只考虑在两个给定素数处最大的阶数。这个结果推广了Sarnak在实二次情况下的工作。这似乎是类数的第一个渐近结果，次数大于2的数域。
Abstract In this paper it is shown that the sum of class numbers of orders in complex cubic fields obeys an asymptotic law similar to the prime numbers as the bound on the regulators tends to infinity. Here only orders are considered which are maximal at two given primes. This result extends work of Sarnak in the real quadratic case. It seems to be the first asymptotic result on class numbers for number fields of degree higher than two.