Article Dans Une Revue Hardy-Ramanujan Journal Année : 1988

Some local-convexity theorems for the zeta-function-like analytic functions

Résumé

In this paper we investigate lower bounds for I(σ)=HH|f(σ+it0+iv)|kdv,
where f(s) is analytic for s=σ+it in R={aσb,t0Htt0+H} with |f(s)|M for sR. 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.
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Dates et versions

hal-01104306 , version 1 (16-01-2015)

Identifiants

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R Balasubramanian, K Ramachandra. Some local-convexity theorems for the zeta-function-like analytic functions. Hardy-Ramanujan Journal, 1988, Volume 11 - 1988, pp.1 - 12. ⟨10.1090/conm/210/02800⟩. ⟨hal-01104306⟩
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