Weierstrass semigroups and automorphism group of a maximal function field with the third largest possible genus, q ≡ 1 3
arxiv(2024)
Abstract
In this article we continue the work started in arXiv:2303.00376v1,
explicitly determining the Weierstrass semigroup at any place and the full
automorphism group of a known 𝔽_q^2-maximal function field Y_3
having the third largest genus, for q ≡ 1 3. This function field
arises as a Galois subfield of the Hermitian function field, and its uniqueness
(with respect to the value of its genus) is a well-known open problem. Knowing
the Weierstrass semigroups may provide a key towards solving this problem.
Surprisingly enough, Y_3 has many different types of Weierstrass semigroups
and the set of its Weierstrass places is much richer than its set of
𝔽_q^2-rational places. We show that a similar exceptional
behaviour does not occur in terms of automorphisms, that is,
Aut(Y_3) is exactly the automorphism group inherited from the
Hermitian function field, apart from small values of q.
MoreTranslated text
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined