Growth of frequently Birkhoff-universal functions of exponential type on rays

TL;DR

This paper investigates the growth behavior of frequently Birkhoff-universal functions of exponential type along different rays, extending known results by analyzing their indicator functions and diagrams.

Contribution

It introduces new growth conditions for these functions based on their indicator functions, expanding previous maximum modulus-based results.

Findings

Extended growth results for Birkhoff-universal functions

Analyzed indicator diagrams and functions for these functions

Provided new criteria for growth along rays

Abstract

We consider growth conditions for (frequently) Birkhoff-universal functions of exponential type with respect to the different rays emanating from the origin. For that purpose, we investigate their (conjugate) indicator diagram or, equivalently, their indicator function. Some known results, where growth is measured with respect to the maximum modulus, are extended.