Sequences of numbers generated by addition in formal groups and new primality and factorization tests
type: Item
instance of: scholarly article
title: Sequences of numbers generated by addition in formal groups and new primality and factorization tests
zbMATH Open document ID: 0614.10004
DOI: 10.1016/0196-8858(86)90023-0
author: D. V. Chudnovsky
author: G. V. Choodnovsky
published in: Advances in Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The authors give a comprehensive study of the relation of algebroid formal group laws to primality and factorization. The Fermat test and the Lucas test were perceived as special cases once the Lenstra test was studied. The addition law of elliptic curves in Weierstrass form is subject to a very detailed analysis, as well as other implementations, e.g., in Jacobi form. New results are also given for factoring \(n=\text{Norm}(\alpha)\) in K/\({\mathbb{Q}}\) based on the (partial) factorization of \(\text{Norm}(\alpha \pm 1)\). Elliptic divisibility sequences of Ward are also used for factorization and to make lists of probable primes. In conclusion, the authors make the programmatic remark: ''A large field for future studies is opened by the possibility of considering other algebraic laws of addition related to the Frobenius operator (say, cubic surfaces or other intermediate Jacobians)''. There is a rather large bibliography of classical and contemporary sources, and it is very difficult to select a subset to cite because of the breadth of the article.
reviewed by: Harvey Cohn
Mathematics Subject Classification ID: 11Y11
Mathematics Subject Classification ID: 11Y05
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 11G10
Mathematics Subject Classification ID: 14L05
zbMATH DE Number: 3993667
zbMATH Keywords: primality tests
zbMATH Keywords: implementations
zbMATH Keywords: factorization algorithms
zbMATH Keywords: abelian varieties
zbMATH Keywords: computational number theory
zbMATH Keywords: formal group laws
zbMATH Keywords: elliptic curves
zbMATH Keywords: bibliography
MaRDI profile type: Publication
full work available at URL: 0196-8858(86)90023-0
OpenAlex ID: W2009129512
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