Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Dobrovolskaya L. P., Dobrovolsky M. N., Dobrovolskii N. N., Rebrova I. Y. Some Questions of Number-theoretical Method in Approximation Analysis. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 4, pp. 47-52. DOI: 10.18500/1816-9791-2013-13-4-47-52

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.11.2013
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Language: 
Russian
Heading: 
Mathematics
UDC: 
511.9
DOI: 
10.18500/1816-9791-2013-13-4-47-52

Some Questions of Number-theoretical Method in Approximation Analysis

Autors: 
Dobrovolskaya Larisa Petrovna, Institute of Economics and Management
Dobrovolsky Mikhail Nikolaevich, Geophysical center RAS
Dobrovolskii Nikolai Nikolaevich, Tula State University, Russia
Rebrova Irina Yurievna, Tula State University, Russia
Abstract: 

This article gives an overview of several actual problems of optimal coefficients method. This overview was done on September 12, 2013 on XI internation conference «Algebra and number theory: modern problems and applications» in Saratov city.

Key words: 
optimal coefficients method
algebraic lattices
Gelfond theorem
hyperbolic zeta-function
References: 
  1. Korobov N. M. Teoretiko-chislovye metody v priblizhennom analize [Number-theoretic methods in approximations analysis]. Moscow, 2004 (in Russian).
  2. Dobrovolskiy N. M. Giperbolicheskaia dzeta-funktsiia reshetok [Hyperbolic zeta-function on lattices]. Tula, 1984. Dep. v VINITI 24.08.84, no. 6090–84 (in Russian).
  3. Dobrovolskaya L. P., Dobrovolskiy M. N., Dobrovolskiy N. M., Dobrovolskiy N. N. Giperbolicheskie dzetafunktsii setok i reshetok i vychislenie optimal’nykh koeffitsientov [Hyperbolic zeta-functions on nets and lattices and computation of optimal coefficients]. Chebyshevskii sbornik [Chebyshev collection], 2012, vol. 13, iss. 4(44), pp. 4–107 (in Russian).
  4. Dobrovolskaya L. P., Dobrovolskiy M. N., Dobrovolskiy  N. M., Dobrovolskiy N. N. Mnogomernye teoretikochislovye setki i reshetki i algoritmy poiska optimal’nykh koeffitsientov [Multidimensional number-theoretic nets
  5. and lattices and their applications]. Tula, State Pedagogic University Press, 2005, 195 p. (in Russian).
  6. Dobrovolskiy N. M. Mnogomernye teoretiko-chislovye setki i reshetki i ikh prilozheniia [Multidimensional number-theoretic nets and lattices and their applications]. Tula, State Pedagogic University Press, 2005, 195 p. (in
  7. Russian).
  8. Dobrovolskiy M. N. Funktsional’noe uravnenie dlia giperbolicheskoi dzeta-funktsii tselochislennykh reshetok [Functional equation of hyperbolic zeta-function on integral lattices]. Vestn. Mosk. un-ta. Ser. 1. Matematika. Mekhanika, 2007, iss. 3, pp. 18–23 (in Russian).
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