\(\ell\)-torsion in class groups of certain families of \(D_4\)-quartic fields

DOI10.5802/jtnb.1109zbMath1453.11136arXiv1808.02148OpenAlexW3080206762MaRDI QIDQ2199670

Chen An

Publication date: 14 September 2020

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.02148

zbMATH Keywords

class-group torsionquartic fields, dihedral fields

Mathematics Subject Classification ID

Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29)

Related Items (5)

ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group ⋮ Pointwise bound for \(\ell \)-torsion in class groups: elementary abelian extensions ⋮ Averages and higher moments for the \(\ell\)-torsion in class groups ⋮ Counting problems: class groups, primes, and number fields ⋮ An approximate form of Artin's holomorphy conjecture and non-vanishing of Artin \(L\)-functions

Cites Work

• A symplectic case of Artin's conjecture
• On \(\ell\)-torsion in class groups of number fields
• Integral bases for quartic fields with quadratic subfields
• Zeros of families of automorphic \(L\)-functions close to 1.
• An effective Chebotarev density theorem for families of number fields, with an application to \(\ell \)-torsion in class groups
• A unified and improved Chebotarev density theorem
• Average bounds for the \(\ell\)-torsion in class groups of cyclic extensions
• Bounds for the ℓ-torsion in class groups
• Averages and moments associated to class numbers of imaginary quadratic fields
• Reflection Principles and Bounds for Class Group Torsion
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