Estimates of lengths of shortest nonzero vectors in some lattices. II
type: Item
instance of: scholarly article
title: Estimates of lengths of shortest nonzero vectors in some lattices. II
author: Alexander S. Rybakov
published in: Discrete Mathematics and Applications
publication date: 2022-10-12T00:00:00Z
review text: The paper considers the minimum norm of 5-dimensional lattices \(L(a,W)\) spanned by the rows of \[\left( \begin{array}{ccccc} W & 0 & 0 & \ldots & 0 \\ a & -1 & 0 & \ldots & 0 \\ a^2 & 0 & -1 & \ldots & 0 \\ \vdots & \vdots & \ddots & \ddots & \vdots \\ a^4 & 0 & \ldots & 0 & =1 \end{array} \right) \] where \(W >0\), \(a \in [0,\ldots,W] \) are given integers. It is shown that for any sufficiently large number \(W\) and any positive \(\varepsilon < 1/1157\) and all but \(W^{1-\varepsilon} \) values of \(a\) the mininum is \(\min (L(a,W)) \geq W^{(1/5-\varepsilon)}\). For Part I see [the author, ibid. 32, No. 3, 207--218 (2022; Zbl 07596775); translation from Diskretn. Mat. 33, No. 1, 31--46 (2021)].
reviewed by: Gabriele Nebe
Mathematics Subject Classification ID: 11H06
Mathematics Subject Classification ID: 11H50
zbMATH DE Number: 7600139
zbMATH Keywords: lattice
zbMATH Keywords: shortest nonzero vectors
zbMATH Keywords: Minkowski successive minima
MaRDI profile type: Publication
full work available at URL: dma-2022-0028
OpenAlex ID: W4304204643
cites work: An Introduction to the Geometry of Numbers
cites work: Q3248054
cites work: The shortest vectors of lattices connected with a linear congruent generator
cites work: Estimates of lengths of shortest nonzero vectors in some lattices. I
cites work: Q3661665
cites work: Reconstructing Truncated Integer Variables Satisfying Linear Congruences
DOI: 10.1515/DMA-2022-0028
description: scientific article; zbMATH DE number 7600139