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

School of Computing

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

18 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

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On the distribution of points on multidimensional modular hyperbolas

Abstract

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