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.
|Number of pages||5|
|Journal||Proceedings of the Japan Academy Series A: Mathematical Sciences|
|Publication status||Published - Mar 2007|