Small prime power residues modulo $p$

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

Let $p$ be a prime number. For each positive integer $k\ge 2$, it is widely believed that the smallest prime that is a $k$th power residue modulo $p$ should be $O(p^{ϵ})$, for any $ϵ>0$. Elliott proved that such a prime is at most $p^{\frac{k-1}{4}+ϵ}$, for each $ϵ>0$. 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 $[1,p^{\frac{k-1}{4}+ϵ}]$ for $ϵ>0$.