Assuming GRH, with Järviniemi and Sgobba we have obtained very general results on Artin-type problems, and with Shparlinski we have discovered uniform bounds on Artin's density. We will address this and also the computational problem of determining a primitive root modulo p by
testing candidates.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/asymptotic25