Artin conjecture
# Artin conjecture

In mathematics, there are several conjectures made by Emil Artin:

* Artin conjecture (L-functions)
* Artin's conjecture on primitive roots
* The (now proved) conjecture that finite fields are quasi-algebraically closed; see Chevalley–Warning theorem
* The (now disproved) conjecture that any algebraic form over the p-adics of degree d in more than $d^2$ variables represents zero: that is, that all p-adic fields are $C_2;$ see Ax–Kochen theorem or Brauer's theorem on forms.
* Artin had also conjectured Hasse's theorem on elliptic curves
