Geodesic
Approximation of quadratic algebraic lattices by integer lattices~---~II
Čebyševskij sbornik, Tome 21 (2020) no. 3, pp. 215-222.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 the discriminant $d$ — of a square-free natural number. 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 grids, quality function, generalized parallelepipedal grid. 
@article{CHEB_2020_21_3_a16,
     author = {A. N. Kormacheva},
     title = {Approximation of quadratic algebraic lattices by integer {lattices~---~II}},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {215--222},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a16/}
}
TY  - JOUR
AU  - A. N. Kormacheva
TI  - Approximation of quadratic algebraic lattices by integer lattices~---~II
JO  - Čebyševskij sbornik
PY  - 2020
SP  - 215
EP  - 222
VL  - 21
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a16/
LA  - ru
ID  - CHEB_2020_21_3_a16
ER  - 
%0 Journal Article
%A A. N. Kormacheva
%T Approximation of quadratic algebraic lattices by integer lattices~---~II
%J Čebyševskij sbornik
%D 2020
%P 215-222
%V 21
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a16/
%G ru
%F CHEB_2020_21_3_a16
A. N. Kormacheva. Approximation of quadratic algebraic lattices by integer lattices~---~II. Čebyševskij sbornik, Tome 21 (2020) no. 3, pp. 215-222. http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a16/

[1] Vronskaya G.T., Dobrovol'skii N., Deviations of flat grids, monograph, ed. N.M. Dobrovol'skii, Tula, 2012

[2] H. Davenport, The higher arithmetic, Nauka, M., 1965, 176 pp.

[3] Kassels D., Introduction to the geometry of numbers, Mir, M., 1965

[4] A. N. Kormacheva, “About the partial quotients of one of the continued fractions”, Chebyshevskii sbornik, 20:1 (2019), 293–301

[5] A. N. Kormacheva, “Approximation of quadratic algebraic lattices by integer lattices”, Chebyshevskii sbornik, 20:2 (2019), 366–373 | MR | Zbl

[6] A. V. Mikhlyaeva, “Approximation of quadratic algebraic lattices and nets by integer lattices and rational nets”, Chebyshevskii sbornik, 19:3 (2018), 241–256 | Zbl

[7] A. V. Mikhlyaeva, “Quality function for the approximation of quadratic algebraic nets”, Chebyshevskii sbornik, 20:1 (2019), 302–307

[8] A. V. Mikhlyaeva, “Quality function for the approximation of quadratic algebraic nets — II”, Chebyshevskii sbornik, 21:3 (2020), 223–231 | MR

[9] A. V. Rodionov, “Hyperbolic parameter of approximation of quadratic algebraic lattices by integers”, Chebyshevskii sbornik, 21:3 (2020), 241–249 | MR | Zbl

[10] H. Hasse, Lectures on number theory, Foreign literature, M., 1953, 528 pp. | MR