Small prime 𝑘-th power residues modulo 𝑝

Kübra Benli
Institut Élie Cartan Lorraine
https://kubrakbenli.wixsite.com/kubrabenli

Date(s) : 01/03/2022   iCal
11 h 00 min - 12 h 00 min

Let 𝑝 be a prime number. For each positive integer 𝑘 ≥ 2, it is widely believed that the smallest prime that is a 𝑘th power residue modulo 𝑝 should be 𝑂(𝑝^ε), for any ε > 0.
Elliott proved that such a prime is at most 𝑝^{(𝑘-1)/4+ε}, for each ε > 0.
In this talk, we discuss the number of prime 𝑘th power residues modulo 𝑝 in the interval [1, 𝑝^{(𝑘-1)/4+ε}] for ε > 0.

Emplacement
Site Sud, Luminy, Ancienne BU, Salle Séminaire2 (RdC)

Catégories

• Séminaire Ernest