Geodesic
Counting the Number of Integral Points in General $n$ -Dimensional Tetrahedra and Bernoulli Polynomials
Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 229-241

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DOI

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.
DOI : 10.4153/CMB-2003-023-0
Mots-clés : 11B75, 11H06, 11P21, 11Y99 
Lin, Ke-Pao; Yau, Stephen S.-T. Counting the Number of Integral Points in General $n$ -Dimensional Tetrahedra and Bernoulli Polynomials. Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 229-241. doi: 10.4153/CMB-2003-023-0
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     author = {Lin, Ke-Pao and Yau, Stephen S.-T.},
     title = {Counting the {Number} of {Integral} {Points} in {General} $n$ {-Dimensional} {Tetrahedra} and {Bernoulli} {Polynomials}},
     journal = {Canadian mathematical bulletin},
     pages = {229--241},
     year = {2003},
     volume = {46},
     number = {2},
     doi = {10.4153/CMB-2003-023-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-023-0/}
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