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 language | English |
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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 | |
Publication status | Published - Mar 2007 |