On a problem of Mahler in the geometry of numbers
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- by A. C. Woods PDF
- Proc. Amer. Math. Soc. 39 (1973), 86-88 Request permission
Abstract:
If $K$ is a convex body in ${R_n}$ and $K(t)$ is that part of $K$ which satisfies $|{x_n}| \leqq t$, 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
- R. P. Bambah, An analogue of a problem of Mahler, Res. Bull. Panjab Univ. 109 (1957), 299–302. MR 97029
- Kurt Mahler, On a problem in the geometry of numbers, Rend. Mat. e Appl. (5) 14 (1954), 38–41. MR 67937
Additional Information
- © Copyright 1973 American Mathematical Society
- 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