(Redirected from Prime Zeta Function)
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The
prime zeta function, usually abbreviated
, is defined as
-
where the sum is over all
primes .
Specific values
- (A085548)
- (A085548)
- (A085964)
Divergence of P(1)
The sum of reciprocals of primes
diverges, since by Fubini’s theorem
-
where
is the
prime counting function.
In particular
-
as proved by Mertens. In fact Mertens gave an explicit error term which was
; modern techniques improve this to
-
unconditionally, or
-
conditionally on the RH.
See also
External Links