Abstract
In this paper, we study a Howe curve $C$ in positive characteristic $p \geq 3$ which is of genus 3 and is hyperelliptic. We will show that if $C$ is superspecial, then its standard form is maximal or minimal over $\mathbf{F}_{p^2}$ without taking its $\mathbf{F}_{p^2}$-form.
Acknowledgment
This paper was written while the author was a Ph.D. student at Yokohama National University, and I would like to express my special thanks to my supervisor Prof. Shushi Harashita for his guidance. The author thanks Toshiyuki Katsura and Tomoyoshi Ibukiyama for their helpful comments.
Citation
Ryo Ohashi. "On the maximality of hyperelliptic Howe curves of genus 3." Kodai Math. J. 45 (2) 282 - 294, June 2022. https://doi.org/10.2996/kmj45206
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