Madhu Raka
Articles written in Proceedings – Mathematical Sciences
Volume 107 Issue 4 November 1997 pp 329-361
Positive values of non-homogeneous indefinite quadratic forms of type (1, 4)
Let Г_{r,n—r} denote the infimum of all number Г > 0 such that for any real indefinite quadratic form in
Volume 126 Issue 4 October 2016 pp 501-548 Research Article
On conjectures of Minkowski and Woods for $n = 9$
Let $\mathbb{R}^n$ be the $n$-dimensional Euclidean space with $O$ as the origin. Let $\wedge$ be a lattice of determinant 1 such that there is a sphere $\mid X \mid \lt R$ which contains no point of $\wedge$ other than $O$ and has $n$ linearly independent points of $\wedge$ on its boundary. A well known conjecture in the geometry of numbers asserts that any closed sphere in $\mathbb{R}^n$ of radius $\sqrt{n/4}$ contains a point of $\wedge$. This is known to be true for $n\leq 8$. Here we prove a more general conjecture of Woods for $n = 9$ from which this conjecture follows in $\mathbb{R}^9$. Together with a result of McMullen
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