A new inequality for the Hermite constants

Details A new inequality for the Hermite constants A new inequality for the Hermite constants

2006-03-20

arxiv.org/abs/math/0603477v2

International Journal of Number Theory 4, 3 (2008) 363-386

Mathematics

Number Theory

24 pages, to appear in Internation Journal of Number Theory

Scientific paper

We prove an inequality of the form $\gamma_n\geq C_n(\gamma_{n-1})$ giving a
lower bound for the Hermite constant $\gamma_n$ in dimension $n$ in terms of
$\gamma_{n-1}$. Iterating this inequality yields a new proof of the
Minkowski-Hlawka bound.

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