HEIGHTS OF ALGEBRAIC POINTS LYING ON CURVES OR HYPERSURFACES

Our first aim will be to give an explicit version of a generalization of the results of Zhang and Zagier on algebraic points (x, y) with x y + 1 = 0. Secondly, we will show that distinct algebraic points lyin g on a given curve of certain type can be distinguished in terms of so me height functions. Thirdly, we will derive a bound for the number of points on such a curve whose heights are under a given bound and whos e coordinates lie in a multiplicative group of given rank.