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2 results

  • Corrigendum: on the mean 3-rank of quadratic fields

  • K. Belabas
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 5 / September 2004
    Published online by Cambridge University Press:
    04 December 2007, p. 1221
    Print publication:
    September 2004
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  • This corrigendum corrects a mistake in K. Belabas, On the mean 3-rank of quadratic fields, Compositio Math. 118 (1999), 1–9.

  • On the Mean 3-Rank of Quadratic Fields

  • KARIM BELABAS
  • Journal:
    Compositio Mathematica / Volume 118 / Issue 1 / August 1999
    Published online by Cambridge University Press:
    04 December 2007, pp. 1-9
    Print publication:
    August 1999
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  • The Cohen–Lenstra–Martinet heuristics give precise predictions about the class groups of a ’random‘ number field. The 3-rank of quadratic fields is one of the few instances where these have been proven. We prove that, in this case, the rate of convergence is at least sub-exponential. In addition, we show that the defect appearing in Scholz‘s mirror theorem is equidistributed with respect to a twisted Cohen–Lenstra density.