The Ramanujan Journal

, Volume 19, Issue 1, pp 71–77 | Cite as

Quadratic fields with noncyclic 5- or 7-class groups



We shall show that the number of quadratic fields with absolute discriminant ≤x and noncyclic 5- or 7-class group is ≫x 1/4 improving the existing known bound \(\gg x^{\frac{1}{5}-\epsilon}\) for g=5 and \(\gg x^{\frac{1}{7}-\epsilon}\) for g=7 in Byeon (Ramanujan J. 11:159–163, 2006).


Noncyclic ideal class groups Quadratic fields 

Mathematics Subject Classification (2000)

11R11 11R29 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsSeoul National UniversitySeoulKorea

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