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December 4, 2025Proceedings of the American Mathematical Society

Counting abelian extensions by Artin–Schreier conductor

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Authors

FGFabian Gundlach

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Overview

This analysis counts abelian extensions using Artin–Schreier conductor, suggesting insights into class field theory.

Key Points

  • The study counts the abelian extensions via the Artin–Schreier conductor, yielding a rational generating function.
  • Counting problem encompasses étale G-extensions of global rational function fields of characteristic p, yielding exact solutions.
  • The approach provides a detailed treatment of generating functions and contrasts with those from class field theory.
  • The rational generating function has implications about geometric interpretations, inviting further exploration of these concepts.

Cite This Study

Fabian Gundlach (2025) studied this question.

synapsesocial.com/papers/6930e8dbea1aef094cca3c3fhttps://doi.org/10.1090/proc/17440
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Synapse has enriched 2 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1On the asymptotics of elementary-abelian extensions of local and global function fields2025 · 1 citations
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