June 27, 2023
Title: On Artin's Primitive Root Conjecture for Function Fields over F_q
Speaker: Leonhard Hochfilzer (Göttingen)
Artin's primititive root conjecture states that any integer g which is not a unit nor a square generates the cyclic multiplicative group (Z/pZ)* for infinitely many primes p. Similarly one may formulate such a problem over global function fields, which was first considered by Herbert Bilharz in the 1930s who achieved partial results. In this talk I will report on joint work with Ezra Waxman where we complete the proof of Artin's primitive root conjecture for function fields over a finite field and generalise the proof to a version of the conjecture for function fields of arbitrary transcendence degree.