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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On a problem of Mahler in the geometry of numbers


Author: A. C. Woods
Journal: Proc. Amer. Math. Soc. 39 (1973), 86-88
MSC: Primary 10E05
DOI: https://doi.org/10.1090/S0002-9939-1973-0335442-X
MathSciNet review: 0335442
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Abstract: If $ K$ is a convex body in $ {R_n}$ and $ K(t)$ is that part of $ K$ which satisfies $ \vert{x_n}\vert \leqq t$, Mahler [2] has shown that $ \Delta K(t)/t$ is a decreasing function of $ t$, where $ \Delta (K)$ is the critical determinant of $ K$. We generalise Mahler's result in a way different from that conjectured by him.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0335442-X
Article copyright: © Copyright 1973 American Mathematical Society