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Mat. Zametki, 1972, Volume 11, Issue 6, Pages 619–623 (Mi mz9829)  

This article is cited in 1 scientific paper (total in 1 paper)

Asymptotic number of solutions of some systems of diophantine inequalities

V. I. Bernik

Institute of Mathematics, Academy of Sciences of the Belorussian SSR

Abstract: The problem of finding the asymptotic number of solutions of the system of inequalities
\begin{gather*} ||\alpha_iq||<q^{-\sigma_i}\qquad(i=1,…,n),\quad\sigma_i>0,
\sigma=\sum_{i=1}^n\sigma_i<c(\alpha_1,…,\alpha_n),\qquad q=1,…,N,
\end{gather*}
is solved under the assumption that for real numbers $\alpha_1,…,\alpha_n$, starting from some $Q=\max(q_1,…,q_n)$ the inequality
$$ ||\alpha_1q_1+…+\alpha_nq_n||\geqslant\frac1{Q^{n+\lambda}} $$
holds for any real $\lambda\geqslant0$.

Full text: PDF file (459 kB)

English version:
Mathematical Notes, 1972, 11:6, 378–380

Bibliographic databases:

UDC: 511
Received: 11.02.1971

Citation: V. I. Bernik, “Asymptotic number of solutions of some systems of diophantine inequalities”, Mat. Zametki, 11:6 (1972), 619–623; Math. Notes, 11:6 (1972), 378–380

Citation in format AMSBIB
\Bibitem{Ber72}
\by V.~I.~Bernik
\paper Asymptotic number of solutions of some systems of diophantine inequalities
\jour Mat. Zametki
\yr 1972
\vol 11
\issue 6
\pages 619--623
\mathnet{http://mi.mathnet.ru/mz9829}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=300980}
\zmath{https://zbmath.org/?q=an:0246.10019|0238.10022}
\transl
\jour Math. Notes
\yr 1972
\vol 11
\issue 6
\pages 378--380
\crossref{https://doi.org/10.1007/BF01093721}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. G. Sprindzhuk, “Achievements and problems in Diophantine approximation theory”, Russian Math. Surveys, 35:4 (1980), 1–80  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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