Counting Artin-Schreier curves over finite fields
Several authors have considered the weighted sum of various types of curves of a certain genus g over a finite field k := Fq of characteristic p where p is a prime and q = pm for some positive integer m. These include elliptic curves (Howe), hyperelliptic curves (Brock and Granville), supersingular curves when p = 2 and g = 2 (Van der Geer and Van der Vlught), and hyperelliptic curves of low genus when p = 2 (Cardona, Nart, Pujolàs, Sadornil). We denote this weighted sum ∑[C] 1/|Autk(C)|' where the sum is over k-isomorphism classes of the curves and Autk(C) is the automorphism group of C over ...
(For more, see "View full record.")
Ho, Anne M.