Small prime 𝑘-th power residues modulo 𝑝

KĂŒbra Benli
Institut Élie Cartan Lorraine

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(đ‘Î”), for any Δ > 0.
Elliott proved that such a prime is at most 𝑝(𝑘-1)/4+Δ, for each Δ > 0.
In this talk, we discuss the number of prime 𝑘th power residues modulo 𝑝 in the interval [1, 𝑝(𝑘-1)/4+Δ] for Δ > 0.

Site Sud, Luminy, Ancienne BU, Salle SĂ©minaire2 (RdC)


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