ON A CONJECTURE OF ERDŐS

ON A CONJECTURE OF ERDŐS

Let a be an integer different from 0, ±1, or a perfect square. We consider a conjecture of Erdős which states that #{p:ℓa(p)=r}≪εrε for any ε>0, where ℓa(p) is the order of a modulo p. In particular, we see what this conjecture says about Artin’s primitive root conjecture and compare it to the ge...

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Veröffentlicht in:Mathematika 2012-07, Vol.58 (2), p.275-289
Hauptverfasser: Felix, Adam Tyler, Murty, M. Ram
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description Let a be an integer different from 0, ±1, or a perfect square. We consider a conjecture of Erdős which states that #{p:ℓa(p)=r}≪εrε for any ε>0, where ℓa(p) is the order of a modulo p. In particular, we see what this conjecture says about Artin’s primitive root conjecture and compare it to the generalized Riemann hypothesis and the ABC conjecture. We also extend work of Goldfeld related to divisors of p+a and the order of a modulo p.
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title ON A CONJECTURE OF ERDŐS
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