Class number calculation using Siegel functions

T. Fukuda; Keiichi Komatsu

doi:10.1112/S146115701400014X

Class number calculation using Siegel functions

T. Fukuda, Keiichi Komatsu

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We propose a fast method of calculating the p-part of the class numbers in certain non-cyclotomic ℤ_p-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.

Original language	English
Pages (from-to)	295-302
Number of pages	8
Journal	LMS Journal of Computation and Mathematics
Volume	17
Issue number	SPEC. ISSUE A
DOIs	https://doi.org/10.1112/S146115701400014X
Publication status	Published - 2014

ASJC Scopus subject areas

Mathematics(all)
Computational Theory and Mathematics

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10.1112/S146115701400014X

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title = "Class number calculation using Siegel functions",

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.",

author = "T. Fukuda and Keiichi Komatsu",

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doi = "10.1112/S146115701400014X",

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journal = "LMS Journal of Computation and Mathematics",

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AU - Komatsu, Keiichi

PY - 2014

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AB - 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.

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U2 - 10.1112/S146115701400014X

DO - 10.1112/S146115701400014X

M3 - Article

AN - SCOPUS:84905459615

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SP - 295

EP - 302

JO - LMS Journal of Computation and Mathematics

JF - LMS Journal of Computation and Mathematics

IS - SPEC. ISSUE A

ER -

Class number calculation using Siegel functions

Abstract

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