Artin conjecture - AbsoluteAstronomy.com

In mathematics, there are several conjectures made by Emil Artin

Emil Artin

Emil Artin was an Austrian-American mathematician of Armenian descent.-Parents:Emil Artin was born in Vienna to parents Emma Maria, née Laura , a soubrette on the operetta stages of Austria and Germany, and Emil Hadochadus Maria Artin, Austrian-born of Armenian descent...

Artin conjecture (L-functions)
Artin's conjecture on primitive roots
Artin's conjecture on primitive roots
In number theory, Artin's conjecture on primitive roots states that a given integer a which is not a perfect square and not −1 is a primitive root modulo infinitely many primes p. The conjecture also ascribes an asymptotic density to these primes...
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. For this see Ax–Kochen theorem
Ax–Kochen theorem
The Ax–Kochen theorem, named for James Ax and Simon B. Kochen, states that for each positive integer d there is a finite set Yd of prime numbers, such that if p is any prime not in Yd then every homogeneous polynomial of degree d over the p-adic numbers in at least d2+1 variables has a nontrivial...

or Brauer's theorem on forms.
Artin had also conjectured Hasse's theorem on elliptic curves

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