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The number of imaginary quadratic fields with a given class number

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

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