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March 8, 2026The Ramanujan JournalOpen Access

Class number relations in almost abelian number fields

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Authors

SBSaad El Boukhari

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Overview

This research examines class number relations through equivariant L-functions in imaginary quadratic fields, indicating new insights on abelian extensions.

Key Points

  • This work aims to explore the relationships between class numbers in almost abelian number fields and leading terms of equivariant Artin L-functions.
  • Introduced a module based on leading terms of equivariant L-functions and Dirichlet regulator.
  • Computed the generalized index relative to the torsion-free part of the unit group.
  • Provided p-adic refinements using idempotents from higher Stark theory.
  • Established that the generalized index equals the ratio of class numbers h_F/h_k.
  • Derived obstructions to integral higher Stark elements mapping to equivariant L-values.
  • Proved class number divisibility under non-decomposition conditions for ramified places.

Cite This Study

Saad El Boukhari (2026) studied this question.

synapsesocial.com/papers/69ada885bc08abd80d5bb888https://doi.org/10.1007/s11139-026-01354-0
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Effective Brauer-Siegel theorems for Artin $L$-functions2025
  2. 2Balanced triple product $p$-adic $L$-functions and Stark points2024
  3. 3Equivariant algebraic $\mathrm{K}$-theory and Artin $L$-functions2024
  4. 4Brumer–Stark units and explicit class field theory2024 · 2 citations
  5. 5Counting abelian extensions by Artin–Schreier conductor2025