On the parity of ideal classes over a fixed prime

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2020-01-23 DOI:10.1353/ajm.2020.0003

Jeongho Park

引用次数: 2

Abstract

abstract:For real quadratic number fields, we consider the order of ideal classes of split prime ideals, $P$, whose norm is a fixed rational prime. We collect fundamental discriminants satisfying a trivial condition for $P$ to be principal, and show that for a positive density of such discriminants, the cyclic subgroup of the ideal class group generated by $P$ does not have a 2-part.

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关于固定素数上理想类的奇偶性

文摘：对于实二次数域，我们考虑分裂素数理想的理想类$P$的阶，其范数是固定有理素数。我们收集了满足$P$为主的平凡条件的基本判别式，并证明了对于这种判别式的正密度，由$P$生成的理想子群的循环子群不具有2-部分。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.