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

Canadian mathematical bulletin

关键词: linear map;    selfadjoint operator;    invertible;    positive definite;    numerical range;   

DOI  :  10.4153/CMB-2003-023-0

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Recently there has been tremendous interest in counting the number of integral points in $n$-dimen-sional tetrahedra with non-integralvertices due to its applications in primality testing and factoring in number theory and in singularities theory. The purpose of thisnote is to formulate a conjecture on sharp upper estimate of thenumber of integral points in $n$-dimensional tetrahedra withnon-integral vertices. We show that this conjecture is true forlow 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.

【 授权许可】

Unknown