The shortest vector problem and tame kernels of cyclotomic fields

DOI10.1016/j.jnt.2021.03.022zbMath1470.11320OpenAlexW3157224283WikidataQ114157042 ScholiaQ114157042MaRDI QIDQ2039518

Chaochao Sun, Kejian Xu, Long Zhang, Zhaopeng Dai

Publication date: 5 July 2021

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2021.03.022

zbMATH Keywords

tame kernelLLL-algorithmSVP

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Cyclotomic extensions (11R18) (K)-theory of global fields (11R70) Quadratic forms (reduction theory, extreme forms, etc.) (11H55) Symbols and arithmetic ((K)-theoretic aspects) (19F15)

Cites Work

• Generators and relations for \(K_{2}O_{F}\)
• On Lovász' lattice reduction and the nearest lattice point problem
• Factoring polynomials with rational coefficients
• Generalization of Thue's theorem and computation of the group \(K_ 2 O_ F\)
• Computation of \(K_ 2\mathbb{Z}[\sqrt {-6}\)]
• Computation of \(K_ 2\mathbb{Z}[\frac{1+\sqrt{-35}}{2}\)]
• The tame kernel of $\mathbb {Q}(\zeta _{5})$ is trivial
• Improved Methods for Calculating Vectors of Short Length in a Lattice, Including a Complexity Analysis
• Elements of small order in K2F
• How to Calculate Shortest Vectors in a Lattice
• Tame and wild kernels of quadratic imaginary number fields
• Computing the tame kernel of quadratic imaginary fields
• Closest point search in lattices
• Computing the Tame Kernel of ℚ(ζ₈)
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