Artin conjecture explained

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 d² variables represents zero: that is, that all p-adic fields are C₂; see Ax–Kochen theorem or Brauer's theorem on forms.
• Artin had also conjectured Hasse's theorem on elliptic curves