素数导体实阿贝尔场类数的不可分性

Mathematical Journal of Ibaraki University Pub Date : 2021-01-01 DOI:10.5036/MJIU.53.1

S. Fujima, H. Ichimura

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引用次数: 1

摘要

对于固定整数n≥1，设p = 2n, n + 1为具有奇数素数的素数，设F = F p, r为导体p的实阿贝尔场，阶为r。当n≤21时，利用计算机证明了素数r不能除类数h F (F)，当r为本原根模r时。这推广了Jakubec和Mets在n = 1情况下的结果。

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Indivisibility of the class number of a real abelian field of prime conductor

For a ﬁxed integer n ≥ 1, let p = 2 nℓ + 1 be a prime number with an odd prime number ℓ and let F = F p,ℓ be the real abelian ﬁeld of conductor p and degree ℓ . When n ≤ 21, we show that a prime number r does not divide the class number h F of F whenever r is a primitive root modulo ℓ with the help of computer. This generalizes a result of Jakubec and Mets¨ankyl¨a for the case n = 1.

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Mathematical Journal of Ibaraki University

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