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

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 present the main result.