The number of imaginary quadratic fields with a given class number

K Soundararajan (1)

1 Department of Mathematics [Stanford]

This paper formulates some conjectures for the number of imaginary quadratic fields of a given class number. It establishes an asymptotic formula for the number of such fields with class number below $H$, and also shows that many fields have class numbers lying outside a very thin set.

Mots clés: $L$-functions; class numbers; value distribution

Domaines: Mathématiques [math]

K Soundararajan. The number of imaginary quadratic fields with a given class number. Hardy-Ramanujan Journal, 2007, Volume 30 - 2007, pp.13-18. ⟨10.46298/hrj.2007.157⟩. ⟨hal-01112054⟩