On the distribution of points on multidimensional modular hyperbolas

Igor E. Shparlinski

doi:10.3792/pjaa.83.5

On the distribution of points on multidimensional modular hyperbolas

Igor E. Shparlinski^*

^*Corresponding author for this work

Department of Computing

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

We study the distribution of points on the (n+1)-dimensional modular hyperbola a₁ ⋯ a_n+1 ≡ c (mod q), where q and c are relatively prime integers. In particular, we show that an elementary argument leads to a straight-forward proof of a recent result of T. Zhang and W. Zhang, with a stronger error term. We also use character sums to obtain an asymptotic formula for the number of points in a given box that lie on such hyperbolas.

Original language	English
Pages (from-to)	5-9
Number of pages	5
Journal	Proceedings of the Japan Academy Series A: Mathematical Sciences
Volume	83
Issue number	2
DOIs	https://doi.org/10.3792/pjaa.83.5
Publication status	Published - Mar 2007

Access to Document

10.3792/pjaa.83.5

Link to publication in Scopus

Fingerprint Dive into the research topics of 'On the distribution of points on multidimensional modular hyperbolas'. Together they form a unique fingerprint.

Cite this

@article{79e8e319eab7477698ec01cadc85d2f8,

title = "On the distribution of points on multidimensional modular hyperbolas",

abstract = "We study the distribution of points on the (n+1)-dimensional modular hyperbola a1 ⋯ an+1 ≡ c (mod q), where q and c are relatively prime integers. In particular, we show that an elementary argument leads to a straight-forward proof of a recent result of T. Zhang and W. Zhang, with a stronger error term. We also use character sums to obtain an asymptotic formula for the number of points in a given box that lie on such hyperbolas.",

author = "Shparlinski, {Igor E.}",

year = "2007",

month = mar,

doi = "10.3792/pjaa.83.5",

language = "English",

volume = "83",

pages = "5--9",

journal = "Proceedings of the Japan Academy Series A: Mathematical Sciences",

issn = "0386-2194",

publisher = "Japan Academy",

number = "2",

}

TY - JOUR

T1 - On the distribution of points on multidimensional modular hyperbolas

AU - Shparlinski, Igor E.

PY - 2007/3

Y1 - 2007/3

N2 - We study the distribution of points on the (n+1)-dimensional modular hyperbola a1 ⋯ an+1 ≡ c (mod q), where q and c are relatively prime integers. In particular, we show that an elementary argument leads to a straight-forward proof of a recent result of T. Zhang and W. Zhang, with a stronger error term. We also use character sums to obtain an asymptotic formula for the number of points in a given box that lie on such hyperbolas.

AB - We study the distribution of points on the (n+1)-dimensional modular hyperbola a1 ⋯ an+1 ≡ c (mod q), where q and c are relatively prime integers. In particular, we show that an elementary argument leads to a straight-forward proof of a recent result of T. Zhang and W. Zhang, with a stronger error term. We also use character sums to obtain an asymptotic formula for the number of points in a given box that lie on such hyperbolas.

UR - http://www.scopus.com/inward/record.url?scp=33947301417&partnerID=8YFLogxK

U2 - 10.3792/pjaa.83.5

DO - 10.3792/pjaa.83.5

M3 - Article

AN - SCOPUS:33947301417

VL - 83

SP - 5

EP - 9

JO - Proceedings of the Japan Academy Series A: Mathematical Sciences

JF - Proceedings of the Japan Academy Series A: Mathematical Sciences

SN - 0386-2194

IS - 2

ER -