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Chebyshevskii Sb., 2016, Volume 17, Issue 4, Pages 185–193 (Mi cheb526)  

On A. V. Malyshev's approach to Minkowski's conjecture concerning the critical determinant of the region $|x|^p + |y|^p < 1$ for $p > 1$

N. M. Glazunov

National Aviation University

Abstract: We present A. V. Malyshev's approach to Minkowski's conjecture (in Davis's amendment) concerning the critical determinant of the region $|x|^p + |y|^p <1$ for $p > 1$ and Malyshev's method. In the sequel of this article we use these approach and method to obtain the main result.
Bibliography: 21 titles.

Keywords: critical lattice; critical determinant; Diophantine inequality; Diophantine approximation; distance function; star body; moduli space.

DOI: https://doi.org/10.22405/2226-8383-2016-17-4-185-193

Full text: PDF file (619 kB)
References: PDF file   HTML file

UDC: 511.9
Received: 28.11.2016
Accepted:12.12.2016
Language:

Citation: N. M. Glazunov, “On A. V. Malyshev's approach to Minkowski's conjecture concerning the critical determinant of the region $|x|^p + |y|^p < 1$ for $p > 1$”, Chebyshevskii Sb., 17:4 (2016), 185–193

Citation in format AMSBIB
\Bibitem{Gla16}
\by N.~M.~Glazunov
\paper On A.\,V.~Malyshev's approach to Minkowski's conjecture concerning the critical determinant of the region $|x|^p + |y|^p < 1$ for $p > 1$
\jour Chebyshevskii Sb.
\yr 2016
\vol 17
\issue 4
\pages 185--193
\mathnet{http://mi.mathnet.ru/cheb526}
\crossref{https://doi.org/10.22405/2226-8383-2016-17-4-185-193}
\elib{http://elibrary.ru/item.asp?id=27708216}


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