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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.


References [Enhancements On Off] (What's this?)

  • [1] R. P. Bambah, An analogue of a problem of Mahler, Res. Bull. Panjab Univ. No. 109 (1957), 299-302. MR 20 #3509. MR 0097029 (20:3509)
  • [2] K. Mahler, On a problem in the geometry of numbers, Roma Ist. Naz. Alta Mat. Rend. Mat. e Appl. (5) 14 (1954), 38-41. MR 16, 802. MR 0067937 (16:802a)

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

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