Description |
Abstract:
Artin's primitive root conjecture (1927) states that, for any
integer $a\neq\pm1$ or a perfect square, there are infinitely many primes
$p$ for which a is a primitive root (mod $p$). This conjecture is not
known for any specific $a$. In my talk I will prove the equivalent of this
conjecture unconditionally for general abelian varieties for all $a$.
Moreover, under GRH, I will prove the strong form of Artin's conjecture
(1927) for abelian varieties, i.e., I will prove the density and the
asymptotic formula for the primitive primes.
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