Large values of ζ(s) for 1/2 < Re(s)

Abstract

We investigate large values of the Riemann zeta function within the critical strip. Let 0<θ<1 be given and let σ∈(1/2,1) be fixed. We prove that for all sufficiently large T,maxTθ≤t≤T|ζ(σ+it)|≥exp⁡(Cσ,θ(log⁡T)1−σ(log⁡log⁡T)σ), where Cσ,θ is a positive number depending on σ and θ. This improves the previous result of Aistleitner (2016) [1].