本源导体阿贝尔场的类数奇偶性注记

Mathematical Journal of Ibaraki University Pub Date : 1900-01-01 DOI:10.5036/MJIU.50.15

S. Fujima, H. Ichimura

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引用次数: 3

摘要

让n≥1是整数,让2 2除以n的最高力量。对于一个素数p = 2 n + 1和一个奇怪的质数,让n虚交换领域的导体p和程度2”在问:我们表明,n≤30 n是奇数的相对类数hN当2是一个原始的根模的情况除外(n ') =(27岁,3)和p = 163的帮助下电脑。

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Note on class number parity of an abelian field of prime conductor

Let n ≥ 1 be an integer and let 2 be the highest power of 2 dividing n. For a prime number p = 2n` + 1 with an odd prime number `, let N be the imaginary abelian field of conductor p and degree 2` over Q. We show that for n ≤ 30, the relative class number hN of N is odd when 2 is a primitive root modulo ` except for the case where (n, `) = (27, 3) and p = 163 with the help of computer.

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Mathematical Journal of Ibaraki University

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