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 Chebyshevskii Sb., 2019, Volume 20, Issue 2, Pages 366–373 (Mi cheb776)

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Approximation of quadratic algebraic lattices by integer lattices

A. N. Kormacheva

Tula State L. N. Tolstoy Pedagogical University (Tula)

Abstract: This paper is devoted to the approximation of a quadratic algebraic lattice by an integer lattice. It calculates the distances between a quadratic algebraic lattice and an integer lattice when they are given by the numerator and denominator of a suitable fraction to the square root of a Prime $p$ of the form $p=2$ or $p=4k+3$.
The results of this work allow us to study questions about the best approximations of quadratic algebraic lattices by integer lattices.

Keywords: quadratic fields, approximation of algebraic lattices, metric space of lattices.

 Funding Agency Grant Number Russian Foundation for Basic Research 19-41-710004_ð_à The reported study was funded by RFBR, project number 19-41-710004_r_a.

DOI: https://doi.org/10.22405/2226-8383-2018-20-2-366-373

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UDC: 511.9
Accepted:12.07.2019

Citation: A. N. Kormacheva, “Approximation of quadratic algebraic lattices by integer lattices”, Chebyshevskii Sb., 20:2 (2019), 366–373

Citation in format AMSBIB
\Bibitem{Kor19} \by A.~N.~Kormacheva \paper Approximation of quadratic algebraic lattices by integer lattices \jour Chebyshevskii Sb. \yr 2019 \vol 20 \issue 2 \pages 366--373 \mathnet{http://mi.mathnet.ru/cheb776} \crossref{https://doi.org/10.22405/2226-8383-2018-20-2-366-373}