JournalsrsmupVol. 130pp. 221–282

Le théorème de Schanuel pour un corps non commutatif

  • Gaël Rémond

    Université Grenoble I, Saint-Martin-d'Hères, France
  • Christine Zehrt-Liebendörfer

    Universität Basel, Switzerland
Le théorème de Schanuel pour un corps non commutatif cover
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Abstract

We prove a version of Schanuel's theorem in the noncommutative case: we provide an asymptotic formula for the number of one-dimensional left subspaces of DND^N of height at most HH, where DD is a finite dimensional rational division algebra, NN a positive integer and HH a real number. The height, as considered in a previous paper, is defined with the help of a maximal order in DD and a positive anti-involution. We give a completely explicit main term involving class number, regulator, discriminant and zeta function of DD. We also compute an explicit error term.

Cite this article

Gaël Rémond, Christine Zehrt-Liebendörfer, Le théorème de Schanuel pour un corps non commutatif. Rend. Sem. Mat. Univ. Padova 130 (2013), pp. 221–282

DOI 10.4171/RSMUP/130-9