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Reflection Principles and Bounds for Class Group Torsion

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.