PreprintCC BY 4.0arXiv
An upper bound for an exceptional automorphism group
Abstract
Let q=ph>7 be odd, put m=(q+1)/2, and suppose that i=(m−2)/2 satisfies gcd(i,m)=gcd(i+2,m)=1. For the Fq2-maximal function field ℱi=Fq2(x,y) defined by ym=xi(x2+1), Peter Beelen, Maria Montanucci, Jonathan Niemann, and Luciane Quoos showed that the geometric automorphism group contains a subgroup of order 4(q+1) and conjectured that its order is exactly 4(q+1). We prove this equality by establishing the reverse inequality.
Related
- K3 surfaces with finite automorphism group in positive characteristic
- Enumeration of orientably-regular maps with automorphism group PGam(2,2p) for prime p
- Global vector fields and the automorphism group of regular semisimple Hessenberg varieties
- On the lengths of MDS codes with a two-transitive permutation automorphism group
- A Quadratic Bound for Automorphism Groups of Curves of Positive p-Rank in Odd Characteristic
BibTeX
@misc{zhuang2026upper,
title = {{An upper bound for an exceptional automorphism group}},
author = {Xu Zhuang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.03050},
eprint = {2609.03050},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03050},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An upper bound for an exceptional automorphism group
AU - Xu Zhuang
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2609.03050
UR - https://arxiv.org/abs/2609.03050
AB - Let q=p^h>7 be odd, put m=(q+1)/2, and suppose that i=(m−2)/2 satisfies gcd(i,m)=gcd(i+2,m)=1. For the F_q^2-maximal function field ℱ_i=F_q^2(x,y) defined by y^m=x^i(x^2+1), Peter Beelen, Maria Montanucci, Jonathan Niemann, and Luciane Quoos showed that the geometric automorphism group contains a subgroup of order 4(q+1) and conjectured that its order is exactly 4(q+1). We prove this equality by establishing the reverse inequality.
ER -