摘要
Inspired by Durfee Conjecture in singularity theory, Yau formulated the Yau number theoretic conjecture(see Conjecture 1.3) which gives a sharp polynomial upper bound of the number of positive integral points in an n-dimensional(n≥3) polyhedron. It is well known that getting the estimate of integral points in the polyhedron is equivalent to getting the estimate of the de Bruijn function ψ(x, y), which is important and has a number of applications to analytic number theory and cryptography. We prove the Yau number theoretic conjecture for n = 6. As an application, we give a sharper estimate of function ψ(x, y) for 5≤y < 17, compared with the result obtained by Ennola.
Inspired by Durfee Conjecture in singularity theory, Yau formulated the Yau number theoretic conjecture（see Conjecture 1.3） which gives a sharp polynomial upper bound of the number of positive integral points in an n-dimensional（n≥3） polyhedron. It is well known that getting the estimate of integral points in the polyhedron is equivalent to getting the estimate of the de Bruijn function ψ（x, y）, which is important and has a number of applications to analytic number theory and cryptography. We prove the Yau number theoretic conjecture for n = 6. As an application, we give a sharper estimate of function ψ（x, y） for 5≤y 〈 17, compared with the result obtained by Ennola.
基金
the Start-Up Fund from Tsinghua University, Tsinghua University Initiative Scientific Research Program and National Natural Science Foundation of China (Grant No. 11401335)
