Redaktion: K. Sigmund, G. Greschonig (Univ. Wien, Strudlhofgasse ...

Zahlentheorie 79
Estimates for height functions on elliptic curves
HORST ZIMMER
(gemeinsam mit Susanne Schmitt)
Universität des Saarlandes, Fachrichtung 6.1 Mathematik
Postfach 15 11 50, D-66041 Saarbrücken
zimmer@math.uni-sb.de
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.