Height difference bounds for elliptic curves over number fields Original Research Article

Let E be an elliptic curve over a number field K. Let h be the logarithmic (or Weil) height on E and image be the canonical height on E. Bounds for the difference image are of tremendous theoretical and practical importance. It is possible to decompose image as a weighted sum of continuous bounded functions image over the set of places υ of K. A standard method for bounding image, (due to Lang, and previously employed by Silverman) is to bound each function Ψυ and sum these local ‘contributions’.