The average sizes of two-torsion subgroups in quotients of class groups of cubic fields

2017/01/11 by Zev Klagsbrun, Klagsbrun, Zev
Mathematics · #11R16 #11R29 #11R45 #19F99 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1701.02838

openalex publication_date 2017/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a generalization of a result of Bhargava regarding the average size Cl(K)[2] as K varies among cubic fields. For a fixed set of rational primes S, we obtain a formula for the average size of Cl(K)/⟨ S ⟩[2] as K varies among cubic fields with a fixed signature, where ⟨ S ⟩ is the subgroup of Cl(K) generated by the classes of primes of K above primes in S. As a consequence, we are able to calculate the average sizes of K_2n(O_K)[2] for n > 0 and for the relaxed Selmer group Sel₂^S(K) as K varies in these same families.

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