Approximation of quadratic algebraic lattices by integer lattices
https://doi.org/10.22405/2226-8383-2019-20-2-366-373
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 ???? of the form ???? = 2 or ???? = 4???? + 3.
The results of this work allow us to study questions about the best approximations of
quadratic algebraic lattices by integer lattices.
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 ???? of the form ???? = 2 or ???? = 4???? + 3.
The results of this work allow us to study questions about the best approximations of
quadratic algebraic lattices by integer lattices.
References
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3. Kassels, D. 1965, Vvedenie v geometriyu chisel, [Introduction to the geometry of numbers], Mir, Moscow, Russia.
4. Kormacheva, A. N., 2019, "About the partial quotients of one of the continued fractions" , Chebyshevskii sbornik, vol. 20, no. 2, pp. 293–301.
5. Mikhlyaeva, A. V., 2018, "Approximation of quadratic algebraic lattices and nets by integer lattices and rational nets" , Chebyshevskii sbornik, vol. 19, no. 3, pp. 241–256.
6. Mikhlyaeva, A. V., 2019, "Quality function for the approximation of quadratic algebraic nets" , Chebyshevskii sbornik, vol. 20, no. 1, pp. 302–307.
Review
For citations:
Kormacheva A.N. Approximation of quadratic algebraic lattices by integer lattices. Chebyshevskii Sbornik. 2019;20(2):366-373. (In Russ.) https://doi.org/10.22405/2226-8383-2019-20-2-366-373
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