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

Lin, Ke-Pao ; Yau, Stephen S.-T.

Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 229-241

Résumé

Recently there has been tremendous interest in counting the number of integral points in $n$ -dimensional 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.

Détail

DOI : 10.4153/CMB-2003-023-0

Mots-clés : 11B75, 11H06, 11P21, 11Y99

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