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Counting the Number of Integral Points in General $n$-Dimensional Tetrahedra and Bernoulli Polynomials

  Published:2003-06-01
 Printed: Jun 2003
  • Ke-Pao Lin
  • Stephen S.-T. Yau
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Abstract

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.
MSC Classifications: 11B75, 11H06, 11P21, 11Y99 show english descriptions Other combinatorial number theory
Lattices and convex bodies [See also 11P21, 52C05, 52C07]
Lattice points in specified regions
None of the above, but in this section
11B75 - Other combinatorial number theory
11H06 - Lattices and convex bodies [See also 11P21, 52C05, 52C07]
11P21 - Lattice points in specified regions
11Y99 - None of the above, but in this section
 

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