Uniform bounds for the density in Artin’s conjecture on primitive roots

Date/heure
11 avril 2024
14:30 - 15:30

Lieu
Salle Döblin

Oratrice ou orateur
Antonella Perucca (Université du Luxembourg)

Catégorie d'évènement
Séminaire de Théorie des Nombres de Nancy-Metz


Résumé
We consider Artin’s conjecture on primitive roots over a number field K, reducing an algebraic number αK×. Under GRH, there is a density dens(α) counting the proportion of the primes of K for which α is a primitive root.
This density dens(α) is a rational multiple of an Artin constant A(τ) that depends on the largest integer τ1 such that
α\(K×\)τ.
Supposing that dens(α)0, we provide uniform bounds for the ratio dens(α)/A(τ). This is joint work with Igor Shparlinski. We also present heuristics obtained with Mia Tholl.