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Mat. Zametki, 1998, Volume 63, Issue 3, Pages 363–369 (Mi mz1290)  

This article is cited in 13 scientific papers (total in 13 papers)

Number of lattice points in the hyperbolic cross

N. M. Dobrovol'skii, A. L. Roshchenya

Tula State Pedagogical University

Abstract: An asymptotic formula for the number of points of an arbitrary lattice in the hyperbolic cross is obtained.

DOI: https://doi.org/10.4213/mzm1290

Full text: PDF file (162 kB)
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English version:
Mathematical Notes, 1998, 63:3, 319–324

Bibliographic databases:

UDC: 511.9
Received: 19.02.1996

Citation: N. M. Dobrovol'skii, A. L. Roshchenya, “Number of lattice points in the hyperbolic cross”, Mat. Zametki, 63:3 (1998), 363–369; Math. Notes, 63:3 (1998), 319–324

Citation in format AMSBIB
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\by N.~M.~Dobrovol'skii, A.~L.~Roshchenya
\paper Number of lattice points in the hyperbolic cross
\jour Mat. Zametki
\yr 1998
\vol 63
\issue 3
\pages 363--369
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\crossref{https://doi.org/10.4213/mzm1290}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1631932}
\zmath{https://zbmath.org/?q=an:0931.11038}
\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 3
\pages 319--324
\crossref{https://doi.org/10.1007/BF02317776}
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    This publication is cited in the following articles:
    1. N. M. Dobrovol'skii, A. L. Roshchenya, I. Yu. Rebrova, “Continuity of the hyperbolic zeta function of lattices”, Math. Notes, 63:4 (1998), 460–463  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Griebel, M, “Sparse grids for the Schrodinger equation”, ESAIM-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique, 41:2 (2007), 215  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Adcock B., “Multivariate Modified Fourier Series and Application to Boundary Value Problems”, Numer. Math., 115:4 (2010), 511–552  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Shen J., Wang L.-L., “Sparse Spectral Approximations of High-Dimensional Problems Based on Hyperbolic Cross”, SIAM J. Numer. Anal., 48:3 (2010), 1087–1109  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Huybrechs D., Iserles A., Norsett S.P., “From High Oscillation to Rapid Approximation IV: Accelerating Convergence”, IMA J. Numer. Anal., 31:2 (2011), 442–468  crossref  mathscinet  zmath  isi  scopus  scopus
    6. L. P. Dobrovolskaya, M. N. Dobrovolskii, N. M. Dobrovolskii, N. N. Dobrovolskii, “Giperbolicheskie dzeta-funktsii setok i reshetok i vychislenie optimalnykh koeffitsientov”, Chebyshevskii sb., 13:4 (2012), 4–107  mathnet
    7. Shen J., Wang L.-L., Yu H., “Approximations By Orthonormal Mapped Chebyshev Functions For Higher-Dimensional Problems in Unbounded Domains”, J. Comput. Appl. Math., 265 (2014), 264–275  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Chernov A., Duong Pham, “Sparse Tensor Product Spectral Galerkin Bem For Elliptic Problems With Random Input Data on a Spheroid”, Adv. Comput. Math., 41:1 (2015), 77–104  crossref  mathscinet  zmath  isi  scopus  scopus
    9. N. M. Dobrovolskii, N. N. Dobrovolskii, V. N. Soboleva, D. K. Sobolev, E. I. Yushina, “Giperbolicheskaya dzeta-funktsiya reshetki kvadratichnogo polya”, Chebyshevskii sb., 16:4 (2015), 100–149  mathnet  elib
    10. Chernov A., Dung D., “New Explicit-in-Dimension Estimates For the Cardinality of High-Dimensional Hyperbolic Crosses and Approximation of Functions Having Mixed Smoothness”, J. Complex., 32:1 (2016), 92–121  crossref  mathscinet  zmath  isi  scopus  scopus
    11. N. M. Dobrovolskii, N. N. Dobrovolskii, V. N. Soboleva, D. K. Sobolev, L. P. Dobrovolskaya, O. E. Bocharova, “O giperbolicheskoi dzeta-funktsii Gurvitsa”, Chebyshevskii sb., 17:3 (2016), 72–105  mathnet  elib
    12. Luo X., Xu X., Rabitz H., “On the fundamental conjecture of HDMR: a Fourier analysis approach”, J. Math. Chem., 55:2 (2017), 632–660  crossref  mathscinet  zmath  isi  scopus
    13. Kubus D., Rayyes R., Steil J.J., “Learning Forward and Inverse Kinematics Maps Efficiently”: Kosecka, J, 2018 IEEE/Rsj International Conference on Intelligent Robots and Systems (Iros), IEEE International Conference on Intelligent Robots and Systems, eds. Maciejewski A., Okamura A., Bicchi A., Stachniss C., Song D., Lee D., Chaumette F., Ding H., Li J., Wen J., Roberts J., Masamune K., Chong N., Amato N., Tsagwarakis N., Rocco P., Asfour T., Chung W., Yasuyoshi Y., Sun Y., Maciekeski T., Althoefer K., AndradeCetto J., Chung W., Demircan E., Dias J., Fraisse P., Gross R., Harada H., Hasegawa Y., Hayashibe M., Kiguchi K., Kim K., Kroeger T., Li Y., Ma S., Mochiyama H., Monje C., Rekleitis I., Roberts R., Stulp F., Tsai CH., Zollo L., IEEE, 2018, 5133–5140  isi
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