6. Let Ω= {z ∈ C : Re z > 1}. The Riemann zeta function ζ : Ω → C is given by ∞ ζ(z)= , 1 , nz n=1 where the principal branch of the powers is assumed. Prove that ζ is well deﬁned and...

6. Let Ω=
{
z

∈
C : Re
z

>
1}. The
Riemann zeta function

ζ
: Ω
→
C is given by

∞

ζ(z)= , 1
,

n
z

n=1

where the principal branch of the powers is assumed. Prove that
ζ
is well deﬁned and analytic on Ω. (Hint: Exercise 5 is helpful.)

May 12, 2022

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