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Miklós Schweitzer
2020 Miklós Schweitzer
6
6
Part of
2020 Miklós Schweitzer
Problems
(1)
existence of entire function under certain conditions
Source: Miklos Schweitzer 2020, Problem 6
12/1/2020
Does there exist an entire function
F
:
C
→
C
F \colon \mathbb{C}\to \mathbb{C}
F
:
C
→
C
such that
F
F
F
is not zero everywhere,
∣
F
(
z
)
∣
≤
e
∣
z
∣
|F(z)|\leq e^{|z|}
∣
F
(
z
)
∣
≤
e
∣
z
∣
for all
z
∈
C
z\in \mathbb{C}
z
∈
C
,
∣
F
(
i
y
)
∣
≤
1
|F(iy)|\leq 1
∣
F
(
i
y
)
∣
≤
1
for all
y
∈
R
y\in \mathbb{R}
y
∈
R
, and
F
F
F
has infinitely many real roots.
complex analysis
function