Some local-convexity theorems for the zeta-function-like analytic functions
Résumé
In this paper we investigate lower bounds for I(σ)=∫H−H|f(σ+it0+iv)|kdv,
where f(s) is analytic for s=σ+it in R={a≤σ≤b,t0−H≤t≤t0+H} with |f(s)|≤M for s∈R. Our method rests on a convexity technique, involving averaging with the exponential function. We prove a general lower bound result for I(σ) and give an application concerning the Riemann zeta-function ζ(s). We also use our methods to prove that large values of |ζ(s)| are ``rare'' in a certain sense.
Domaines
Mathématiques [math]Origine | Accord explicite pour ce dépôt |
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