A note on the separated maximum modulus points of meromorphic functions

Abstract

We give an upper estimate of Petrenko's deviation for a meromorphic function of finite lower order in terms of Valiron's defect and the number p(∞, f ) of separated maximum modulus points of the function. We also present examples showing that this estimate is sharp.

On the maximum points and deviations of meromorphic minimal surfaces

“…In 2004 E. Ciechanowicz and I. I. Marchenko applied a quantity measuring the number of separated maximum modulus points of a meromorphic function to obtain an upper estimate of deviation for meromorphic functions ( [5], see also [6] and [7]). We define a similar quantity for meromorphic minimal surfaces.…”

“…where G * t is the symmetric rearrangement of the set G t ( [8]). The function u * ϕ (re iφ ) is non-negative and non-increasing in the interval [0, π], even with respect to ϕ and for each fixed r equimeasurable with u ϕ (re iφ ).…”

Baernstein’s star-function, maximum modulus points and a problem of Erdős

“…In 2021 there will be the 80th birth anniversary of Albert Baernstein II (1941-2014. I was acquainted with him personally and I have been frequently applying his brilliant function (star-function) while solving my research problems.…”