K Soundararajan - The number of imaginary quadratic fields with a given class number

hrj:157 - Hardy-Ramanujan Journal, January 1, 2007, Volume 30 - https://doi.org/10.46298/hrj.2007.157
The number of imaginary quadratic fields with a given class number

Authors: K Soundararajan

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.


Volume: Volume 30
Published on: January 1, 2007
Submitted on: March 3, 2015
Keywords: value distribution,class numbers, $L$-functions,[MATH] Mathematics [math]


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