Reflection Principles and Bounds for Class Group Torsion

  title={Reflection Principles and Bounds for Class Group Torsion},
  author={Jordan S. Ellenberg and Akshay Venkatesh},
We introduce a new method to bound -torsion in class groups, combining analytic ideas with reflection principles. This gives, in particular, new bounds for the 3-torsion part of class groups in quadratic, cubic and quartic number fields, as well as bounds for certain families of higher degree fields and for higher . Conditionally on GRH, we obtain a nontrivial bound for -torsion in the class group of a general number field. 
Highly Cited
This paper has 23 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 13 references

The 3-part of class numbers of quadratic fields.

L. Pierce
Journal of the London Mathematical Society (2) • 2005
View 4 Excerpts
Highly Influenced

The number of elliptic curves over Q with conductor N.

A. Brumer, J. Silverman
Manuscripta Mathematica 91, • 1996
View 4 Excerpts
Highly Influenced

Bounds for arithmetic multiplicities.

W. Duke
Proceedings of the International Congress of Mathematicians. Berlin, • 1998
View 2 Excerpts
Highly Influenced

Effective versions of the Chebotarev density theorem.

J. Lagarias, A. Odlyzko
Algebraic Number Fields: L-functions and Galois Properties, • 1975
View 2 Excerpts
Highly Influenced

Théoremes de réflexion.

G. Gras
Journal Théorie des Nombres de Bordeaux 10, no • 1998
View 2 Excerpts

Note on the class group of algebraic function fields.

M. Madan, D. Madden
Journal Fur Die Reine Und Angewandte Mathematik • 1977
View 2 Excerpts

III . “ Ranks of 3class groups of nonGalois cubic fields . ”

F. Gerth
Acta Arithmetica • 1976

Similar Papers

Loading similar papers…