A computational technique for determining the class number of a pure cubic field-Reference-Cited by-同舟云学术

A computational technique for determining the class number of a pure cubic field

Published:1976 Issue:134 Volume:30 Page:312-323
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Barrucand Pierre,Williams H. C.,Baniuk L.

Abstract

Two different computational techniques for determining the class number of a pure cubic field are discussed. These techniques were implemented on an IBM/370-158 computer, and the class number for each pure cubic field Q ( D 1 / 3 ) Q({D^{1/3}}) for D = 2 , 3 , … , 9999 D = 2,3, \ldots ,9999 was obtained. Several tables are presented which summarize the results of these computations. Some theorems concerning the class group structure of pure cubic fields are also given. The paper closes with some conjectures which were inspired by the computer results.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1976-30-134/S0025-5718-1976-0392913-9/S0025-5718-1976-0392913-9.pdf

Reference15 articles.

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3. A rational genus, class number divisibility, and unit theory for pure cubic fields;Barrucand, Pierre;J. Number Theory,1970

4. Some computer results on units in quadratic and cubic fields;Beach, B. D.,1971

5. The rational solutions of the diophantine equation 𝑌²=𝑋³-𝐷;Cassels, J. W. S.;Acta Math.,1950

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