On the distribution of points on multidimensional modular hyperbolas

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)5-9
Number of pages5
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Volume83
Issue number2
DOIs
Publication statusPublished - Mar 2007

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