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number_theory
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riemann_zeta_function.html
Riemann Zeta-Function
For
s
∈
ℂ
with
ℜ
(
s
)
>
1
, the Riemann zeta-function is defined as
For
s
>
1
,
ζ
(
s
)
=
s
s
−
1
−
s
∫
1
∞
{
x
}
x
s
+
1
d
x
. The integral converges for
s
>
0
, and
lim
s
→
1
+
(
s
−
1
)
ζ
(
s
)
=
1
(Zeta-Function has a simple pole at s=1 with residue 1).