English

Bounds for the relative class number problem for function fields

Number Theory 2025-05-26 v2

Abstract

We establish bounds on a finite separable extension of function fields in terms of the relative class number, thus reducing the problem of classifying extensions with a fixed relative class number to a finite computation. We also solve the relative class number two problem in all cases where the base field has constant field not equal to F2\mathbb{F}_2.

Keywords

Cite

@article{arxiv.2412.12467,
  title  = {Bounds for the relative class number problem for function fields},
  author = {Santiago Arango-Piñeros and María Chara and Asimina S. Hamakiotes and Kiran S. Kedlaya and Gustavo Rama},
  journal= {arXiv preprint arXiv:2412.12467},
  year   = {2025}
}