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

Čebyševskij sbornik, Tome 17 (2016) no. 4, pp. 185-193.

Résumé

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.

Détail

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

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