## 15. ÖMG-Kongress

Jahrestagung der Deutschen Mathematikervereinigung

#### 16. bis 22. September 2001 in Wien

**Sektion 2 - Zahlentheorie**

Donnerstag, 20. September 2001, 14.00, Hörsaal 41

**Estimates for height functions on elliptic curves**
**Horst Zimmer**, **Universität des Saarlandes**
(Koautor: Susanne Schmitt)

There are essentially two height functions on an elliptic curve over a
global field, the naive or Weil height and the canonical or Néron-Tate height.
The first is good for calculations but bad for the theory and the second is,
on the contrary, bad for calculations but good for the theory. It is therefore
worthwile to estimate the difference between the two height functions.
This was done at first by Dem'janenko and the author, later by Silverman and
Siksek. The point is that the Weil height can be modified and, in the number
field case, be replaced by another modified height.

Estimates of the differences between various heights can be obtained in a simple
manner. In particular, it makes sense to compare the estimates given by the
author with those obtained by Silverman and Siksek.

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