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Search: MSC category 11H06 ( Lattices and convex bodies [See also 11P21, 52C05, 52C07] )

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1. CMB 2003 (vol 46 pp. 229)

Lin, Ke-Pao; Yau, Stephen S.-T.
 Counting the Number of Integral Points in General $n$-Dimensional Tetrahedra and Bernoulli Polynomials Recently there has been tremendous interest in counting the number of integral points in $n$-dimen\-sional tetrahedra with non-integral vertices due to its applications in primality testing and factoring in number theory and in singularities theory. The purpose of this note is to formulate a conjecture on sharp upper estimate of the number of integral points in $n$-dimensional tetrahedra with non-integral vertices. We show that this conjecture is true for low dimensional cases as well as in the case of homogeneous $n$-dimensional tetrahedra. We also show that the Bernoulli polynomials play a role in this counting. Categories:11B75, 11H06, 11P21, 11Y99
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