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

Ke-Pao Lin; Xue Luo; Stephen S.-T. Yau; Huaiqing Zuo

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 9, page 1937-1966
- ISSN: 1435-9855

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topLin, 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 -

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