On a number theoretic conjecture on positive integral points in a 5-dimensional tetrahedron and a sharp estimate of the Dickman–De Bruijn function

Lin, Ke-Pao, et al. "On a number theoretic conjecture on positive integral points in a 5-dimensional tetrahedron and a sharp estimate of the Dickman–De Bruijn function." Journal of the European Mathematical Society 016.9 (2014): 1937-1966. <http://eudml.org/doc/277228>.

@article{Lin2014,
abstract = {It is well known that getting the estimate of integral points in right-angled simplices is equivalent to getting the estimate of Dickman-De Bruijn function $\psi (x,y)$ which is the number of positive integers $\le x$ and free of prime factors $>y$. Motivating from the Yau Geometry Conjecture, the third author formulated the Number Theoretic Conjecture which gives a sharp polynomial upper estimate that counts the number of positive integral points in n-dimensional ($n\ge 3$) real right-angled simplices. In this paper, we prove this Number Theoretic Conjecture for $n=5$. As an application, we give a sharp estimate of Dickman-De Bruijn function $\psi (x,y)$ for $5\le y<13$.},
author = {Lin, Ke-Pao, Luo, Xue, Yau, Stephen S.-T., Zuo, Huaiqing},
journal = {Journal of the European Mathematical Society},
keywords = {tetrahedron; Yau number-theoretic conjecture; upper estimate; tetrahedron; Yau number-theoretic conjecture; upper estimate},
language = {eng},
number = {9},
pages = {1937-1966},
publisher = {European Mathematical Society Publishing House},
title = {On a number theoretic conjecture on positive integral points in a 5-dimensional tetrahedron and a sharp estimate of the Dickman–De Bruijn function},
url = {http://eudml.org/doc/277228},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Lin, Ke-Pao
AU - Luo, Xue
AU - Yau, Stephen S.-T.
AU - Zuo, Huaiqing
TI - On a number theoretic conjecture on positive integral points in a 5-dimensional tetrahedron and a sharp estimate of the Dickman–De Bruijn function
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 9
SP - 1937
EP - 1966
AB - It is well known that getting the estimate of integral points in right-angled simplices is equivalent to getting the estimate of Dickman-De Bruijn function $\psi (x,y)$ which is the number of positive integers $\le x$ and free of prime factors $>y$. Motivating from the Yau Geometry Conjecture, the third author formulated the Number Theoretic Conjecture which gives a sharp polynomial upper estimate that counts the number of positive integral points in n-dimensional ($n\ge 3$) real right-angled simplices. In this paper, we prove this Number Theoretic Conjecture for $n=5$. As an application, we give a sharp estimate of Dickman-De Bruijn function $\psi (x,y)$ for $5\le y<13$.
LA - eng
KW - tetrahedron; Yau number-theoretic conjecture; upper estimate; tetrahedron; Yau number-theoretic conjecture; upper estimate
UR - http://eudml.org/doc/277228
ER -