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A proof of Minkowski’s conjecture on the critical determinant of the region \(| x| ^ p+| y| ^ p<1\). (Russian) Zbl 0602.10021
The paper contains a preliminary account of the complete proof of Minkowski’s conjecture concerning the critical determinant of the region \(| x|^ p+| y|^ p<1\). The conjecture is reduced to some inequalities by analytic methods and the obtained inequalities are verified by computers for various values of p. The proof is based on the methods proposed in the following papers: [the third author and A. B. Voronetskij, Acta Arith. 27, 447-458 (1975; Zbl 0302.10028); Tezisy dokladov Vsesoyuznoj konferentsii ”Teoriya chisel i ee prilozheniya”, Tbilisi, 43-45, 47-48 (Russian) (1985; Zbl 0597.10001)], etc.
Reviewer: G.Gogishvili

MSC:
11H16 Nonconvex bodies
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