#### Abstract for the paper

## The exponential rank of nonarchimedean exponential fields

* by Franz-Viktor and Salma Kuhlmann*

For an exponential on a nonarchimedean ordered field, we introduce the
notion of the exponential rank, in analogy to the rank of the field.
This gives information about the growth rate of the exponential, and
about the convex valuations on the field which are compatible with the
exponential. We give several characterizations of these valuations,
using maps induced by the exponential on the value group of the natural
valuation and on the rank of the field. Finally, we construct
exponential fields of arbitrary exponential rank.

*Last update: February 3, 1999*