Critical lattices, elliptic curves and their possible dynamics

Details Critical lattices, elliptic curves and their possible dynamics Critical lattices, elliptic curves and their possible dynamics

2004-01-26

arxiv.org/abs/math/0401358v1

Mathematics

Number Theory

7 pages, Latex

Scientific paper

We present a combinatorial geometry and dynamical systems framework for the investigation and proof of the Minkowski conjecture about critical determinant of the region $ |x|^p + |y|^p < 1, p > 1. $ The application of the framework may drastically reduce the investigation of sufficiently smooth real functions of many variables. Incidentally, we establish connections between critical lattices, dynamical systems and elliptic curves.

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