Surreal numbers, derivations and transseries

Submitted by Vincenzo Mantova on Wed, 04/03/2015 - 19:40
TitleSurreal numbers, derivations and transseries
Publication TypeJournal Article
Year of PublicationIn Press
AuthorsBerarducci, A, Mantova, V
JournalJournal of the European Mathematical Society
Date Published2015/03
Type of Articlepreprint

Several authors have conjectured that Conway's field of surreal numbers, equipped with the exponential function of Kruskal and Gonshor, can be described as a field of transseries and admits a compatible differential structure of Hardy-type. In this paper we give a complete positive solution to both problems. We also show that with this new differential structure, the surreal numbers are Liouville closed, namely the derivation is surjective.

Refereed DesignationRefereed