Natural density of rank-$2$ Drinfeld modules with big Galois image

Chien-Hua Chen

Natural density of rank-$2$ Drinfeld modules with big Galois image

Number Theory 2024-07-26 v3

Authors: Chien-Hua Chen

Abstract

In this paper, we compute the natural density of rank- $1$ Drinfeld module over $\mathbb{F}_q[T]$ with surjective adelic Galois representation; and the natural density of rank- $2$ Drinfeld modules over $\mathbb{F}_q[T]$ whose $\mathfrak{l}$ -adic Galois image containing the special linear subgroup for finitely many prime ideal $\mathfrak{l}$ .

Keywords

Drinfeld modules natural density Galois representations adelic Galois representation special linear subgroup function fields

Cite

@article{arxiv.2403.15109,
  title  = {Natural density of rank-$2$ Drinfeld modules with big Galois image},
  author = {Chien-Hua Chen},
  journal= {arXiv preprint arXiv:2403.15109},
  year   = {2024}
}

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11 pages

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