The mean number of 3-torsion elements in ray class groups of quadratic fields

2016/09/08 by Varma, Ila · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1609.02292

Abstract

We determine the average number of 3-torsion elements in the ray class groups of fixed (integral) conductor c of quadratic fields ordered by absolute discriminant, generalizing Davenport and Heilbronn's theorem on class groups. A consequence of this result is that a positive proportion of such ray class groups of quadratic fields have trivial 3-torsion subgroup whenever the conductor c is taken to be a squarefree integer having very few prime factors none of which are congruent to 1 \bmod 3. Additionally, we compute the second main term for the number of 3-torsion elements in ray class groups with fixed conductor of quadratic fields with bounded discriminant.

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