2024/12/06 by Niemann, Jonathan
Mathematics · #Algebraic Geometry and Number Theory #Advanced Harmonic Analysis Research
paper · pdf · doi:10.48550/arxiv.2412.04952
The classification of maximal function fields over a finite field is a difficult open problem, and even determining isomorphism classes among known function fields is challenging in general. We study a particular family of maximal function fields defined over a finite field with q2 elements, where q is the power of an odd prime. When d := (q+1)/2 is a prime, this family is known to contain a large number of non-isomorphic function fields of the same genus and with the same automorphism group. We compute the automorphism group and isomorphism classes also in the case where d is not a prime.