Abstract: The number F(h) of imaginary quadratic fields with class number h is of classical interest: Gauss' class number problem asks for a determination of those fields counted by F(h). The unconditional computation of F(h) for h x is less or equal to y 100 was completed by M. Watkins, and K. Soundararajan has more recently made conjectures about the order of magnitude of F(h) as h→∞ and determined its average order.
For odd h we refine Soundararajan's conjecture to a conjectural asymptotic formula and also consider the subtler problem of determining the number F(G) of imaginary quadratic fields with class group isomorphic to a given finite abelian group G. [...]
Recording during the thematic meeting: « Dynamics and Graphs over Finite Fields: Algebraic, Number Theoretic and Algorithmic Aspects» the March 31, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
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