JournalsjemsVol. 20, No. 2pp. 339–390

Surreal numbers, derivations and transseries

  • Alessandro Berarducci

    Università di Pisa, Italy
  • Vincenzo Mantova

    Scuola Normale Superiore, Pisa, Italy
Surreal numbers, derivations and transseries cover

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Abstract

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, that is, the derivation is surjective.

Cite this article

Alessandro Berarducci, Vincenzo Mantova, Surreal numbers, derivations and transseries. J. Eur. Math. Soc. 20 (2018), no. 2, pp. 339–390

DOI 10.4171/JEMS/769