{"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}
引用次数: 2
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.
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.
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