Unified treatment of Artin-type problems

Contact: Pieter Moree (moree@mpim-bonn.mpg.de)
 

Artin's Primitive Root Conjecture dates back to 1927. In its most basic form it states that for an integer $a$ (different from $0,1,-1$) that is not a square there exist infinitely many primes $p$ such that $a$ modulo $p$ generates the multiplicative group at $p$.
In 1967, Hooley was able to prove this fact relying on GRH and since then many variants have been considered. In this talk we present a joint work with Järviniemi, where we explain how to deal with a question more general than Artin's Conjecture that unifies several previously considered variants.