Date/heure
20 mai 2021
14:45 - 15:45
Lieu
Salle de séminaire de Théorie des Nombres virtuelle
Oratrice ou orateur
Kübra Benli
Catégorie d'évènement Analyse et théorie des nombres
Résumé
Let $p$ be a prime number. For each positive integer $k\geq 2$, it is widely believed that the smallest prime that is a $k$th power residue modulo $p$ should be $O(p^{\epsilon})$, for any $\epsilon>0$. Elliott proved that such a prime is at most $p^{\frac{k-1}{4}+\epsilon}$, for each $\epsilon>0$. In this talk we discuss the distribution of prime $k$th power residues modulo $p$ in the range $[1, p]$, with a more emphasis on the subrange $[1,p^{\frac{k-1}{4}+\epsilon}]$ for $\epsilon>0$.