Small solutions of congruences over algebraic number fields
type: Item
instance of: scholarly article
title: Small solutions of congruences over algebraic number fields
zbMATH Open document ID: 0608.12001
author: Todd Cochrane
published in: Illinois Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Let \(f_ 1({\mathfrak x}),...,f_ k({\mathfrak x})\) be homogeneous polynomials in n variables over the ring of integers R in a number field, and let A be a nonzero ideal in R. We obtain small solutions to the system of congruences \(f_ 1({\mathfrak x})\equiv \cdot \cdot \cdot \equiv f_ k({\mathfrak x})\equiv 0\) (mod A), the notion of a small point being given two interpretations, a point having coordinates with small norms, and a point having coordinates of small size. Linear systems, quadratic systems, and more general systems are all dealt with.
Mathematics Subject Classification ID: 11R04
Mathematics Subject Classification ID: 11A07
zbMATH DE Number: 3983303
zbMATH Keywords: congruences over algebraic number fields
zbMATH Keywords: homogeneous polynomials
zbMATH Keywords: small solutions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3983303