On class numbers of algebraic function fields defined by \(y^ 2=x^ n+a\) over \(GF(p)\) (Q1196780)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On class numbers of algebraic function fields defined by \(y^ 2=x^ n+a\) over \(GF(p)\) |
scientific article; zbMATH DE number 89552
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On class numbers of algebraic function fields defined by \(y^ 2=x^ n+a\) over \(GF(p)\) |
scientific article; zbMATH DE number 89552 |
Statements
On class numbers of algebraic function fields defined by \(y^ 2=x^ n+a\) over \(GF(p)\) (English)
0 references
16 January 1993
0 references
Let \(K=GF(p)\) be a finite Galois field of characteristic \(p\neq 2\). Let \(F=K(x,y)\) be a function field defined by \(y^ 2=x^ n+a\), where \(a\in K\), \(n\) is a prime number. Let \(h(F)\) denote the (degree-zero divisor) class number and \(g\) the genus of \(F\). The author proves that \(h(F)=p^ g+1\) if \(p\) is congruent to a primitive root modulo \(n\).
0 references
algebraic function field
0 references
hyperelliptic function field
0 references
class number
0 references
0 references
