R Balasubramanian ; K Ramachandra - Some local-convexity theorems for the zeta-function-like analytic functions

hrj:103 - Hardy-Ramanujan Journal, January 1, 1988, Volume 11 - 1988 - https://doi.org/10.46298/hrj.1988.103
Some local-convexity theorems for the zeta-function-like analytic functionsArticle

Authors: R Balasubramanian 1; K Ramachandra 1

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.


Volume: Volume 11 - 1988
Published on: January 1, 1988
Imported on: March 3, 2015
Keywords: local-convexity,functional equation,analytic functions,[MATH]Mathematics [math]

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