报告题目： Artin’s conjecture for abelian varieties Ⅲ 报 告 人： Prof. Cristian Virdol 报告人所在单位： Yonsei University 报告日期： 2017-06-21 星期三 报告时间： 14:00-15:00 报告地点： 光华东主楼2201 报告摘要： 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 $a$. 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. 本年度学院报告总序号： 132