location:  Publications → journals → CMB
Abstract view

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
 Format: HTML LaTeX MathJax PDF PostScript

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 - 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

 top of page | contact us | privacy | site map |