Analysis of sharp polynomial upper estimate of number of positive integral points in a five-dimensional tetrahedra Original Research Article

Let image be real numbers and image be the number of positive integral solutions of image. In this paper we show that image This confirms a conjecture of Durfee for the dimension 5 case. We show also that the upper estimate of image given by Lin and Yau is strictly sharper than that suggested by Durfee conjecture if image, but is not sharper than that suggested by Durfee conjecture if image.