一元解析类数公式的一个应用

Q1 Mathematics

Lms Journal of Computation and Mathematics Pub Date : 2016-01-01 DOI:10.1112/S1461157016000097

C. Fieker, Yinan Zhang

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引用次数: 8

摘要

我们提出了一种验证数字域$K$类数的$p$ -部分的算法，假设$K$是完全实数并且是有理数域$\mathbb{Q}$的阿贝尔扩展，且$p$是任意素数。在4度或更高的域上，该算法已被启发式地证明比计算整个类数的经典算法更快，并且随着域度的增加而提高。

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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An application of the -adic analytic class number formula

We propose an algorithm to verify the $p$ -part of the class number for a number field $K$ , provided $K$ is totally real and an abelian extension of the rational field $\mathbb{Q}$ , and $p$ is any prime. On fields of degree 4 or higher, this algorithm has been shown heuristically to be faster than classical algorithms that compute the entire class number, with improvement increasing with larger field degrees.

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来源期刊

Lms Journal of Computation and Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： LMS Journal of Computation and Mathematics has ceased publication. Its final volume is Volume 20 (2017). LMS Journal of Computation and Mathematics is an electronic-only resource that comprises papers on the computational aspects of mathematics, mathematical aspects of computation, and papers in mathematics which benefit from having been published electronically. The journal is refereed to the same high standard as the established LMS journals, and carries a commitment from the LMS to keep it archived into the indefinite future. Access is free until further notice.