类数计算使用西格尔函数

Q1 Mathematics

Lms Journal of Computation and Mathematics Pub Date : 2014-01-01 DOI:10.1112/s146115701400014x

T. Fukuda, K. Komatsu

{"title":"类数计算使用西格尔函数","authors":"T. Fukuda, K. Komatsu","doi":"10.1112/s146115701400014x","DOIUrl":null,"url":null,"abstract":"We propose a fast method of calculating the p-part of the class numbers in certain non-cyclotomic Zp-extensions of an imaginary quadratic field using elliptic units constructed by Siegel functions. We carried out practical calculations for p = 3 and determined λ-invariants of such Z3-extensions which were not known in our previous paper.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"17 1","pages":"295-302"},"PeriodicalIF":0.0000,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/s146115701400014x","citationCount":"2","resultStr":"{\"title\":\"Class number calculation using Siegel functions\",\"authors\":\"T. Fukuda, K. Komatsu\",\"doi\":\"10.1112/s146115701400014x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose a fast method of calculating the p-part of the class numbers in certain non-cyclotomic Zp-extensions of an imaginary quadratic field using elliptic units constructed by Siegel functions. We carried out practical calculations for p = 3 and determined λ-invariants of such Z3-extensions which were not known in our previous paper.\",\"PeriodicalId\":54381,\"journal\":{\"name\":\"Lms Journal of Computation and Mathematics\",\"volume\":\"17 1\",\"pages\":\"295-302\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1112/s146115701400014x\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lms Journal of Computation and Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1112/s146115701400014x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lms Journal of Computation and Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1112/s146115701400014x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 2

摘要

本文提出了一种利用西格尔函数构造的椭圆单位快速计算虚二次域非分环zp扩展中类数p部分的方法。我们对p = 3进行了实际计算，并确定了这类z3扩展的λ-不变量，这是我们在以前的文章中所不知道的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Class number calculation using Siegel functions

We propose a fast method of calculating the p-part of the class numbers in certain non-cyclotomic Zp-extensions of an imaginary quadratic field using elliptic units constructed by Siegel functions. We carried out practical calculations for p = 3 and determined λ-invariants of such Z3-extensions which were not known in our previous paper.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.