Difference between revisions of "Artin's conjecture on primitive roots"

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(Relation with other conjectures and known facts)
 
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==Relation with other conjectures and known facts==
 
==Relation with other conjectures and known facts==
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| [[Heath-Brown theorem on Artin's conjecture]] || Artin's conjecture holds for all but two exceptional values of <math>a</math>. However, no explicit information about the explicit values of <math>a</math> || Unconditional
 
| [[Heath-Brown theorem on Artin's conjecture]] || Artin's conjecture holds for all but two exceptional values of <math>a</math>. However, no explicit information about the explicit values of <math>a</math> || Unconditional
 
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<section end="related"/>
  
 
==External links==
 
==External links==
  
 
* [http://guests.mpim-bonn.mpg.de/moree/surva.pdf A survey of Artin's conjecture and the developments related to it (PDF)]
 
* [http://guests.mpim-bonn.mpg.de/moree/surva.pdf A survey of Artin's conjecture and the developments related to it (PDF)]

Latest revision as of 04:24, 2 January 2012

Statement

Infinitude version

Suppose is an integer that is not equal to and is not a perfect square, i.e., is not the square of an integer. Then, there exist infinitely many primes such that is a primitive root modulo .

Density version

Fill this in later

Relation with other conjectures and known facts


Name of conjecture/fact Statement Conditional to ...
Hooley's theorem Artin's conjecture holds for all (special cases of) generalized Riemann hypothesis
Gupta-Ram Murty theorem Artin's conjecture holds for infinitely many Unconditional
Heath-Brown theorem on Artin's conjecture Artin's conjecture holds for all but two exceptional values of . However, no explicit information about the explicit values of Unconditional


External links