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Orthogonality Defects of HKZ-Reduced Bases
Abstract
Let Dn denote the supremum of the orthogonality defects over all n-dimensional Hermite--Korkine--Zolotarev (HKZ)-reduced bases. This paper shows that, as n→∞, log Dn=2nlog n−nloglog n+O(n). We also determine the exact value D4=4375/1024.
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BibTeX
@misc{li2026orthogonality,
title = {{Orthogonality Defects of HKZ-Reduced Bases}},
author = {Zhixing Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.22943},
eprint = {2608.22943},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.22943},
}
RIS
TY - UNPB
TI - Orthogonality Defects of HKZ-Reduced Bases
AU - Zhixing Li
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2608.22943
UR - https://arxiv.org/abs/2608.22943
AB - Let D_n denote the supremum of the orthogonality defects over all n-dimensional Hermite--Korkine--Zolotarev (HKZ)-reduced bases. This paper shows that, as n→∞, log D_n=2nlog n−nloglog n+O(n). We also determine the exact value D_4=4375/1024.
ER -