MathDB

existence of entire function under certain conditions

Source: Miklos Schweitzer 2020, Problem 6

December 1, 2020

complex analysisfunction

Problem Statement

Does there exist an entire function

F \colon \mathbb{C}\to \mathbb{C}

such that

F

is not zero everywhere,

|F(z)|\leq e^{|z|}

for all

z\in \mathbb{C}

|F(iy)|\leq 1

for all

y\in \mathbb{R}

, and

F

has infinitely many real roots.