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nomadreid
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- ζ(s)=ζ(1-s) for the zeta function seems to indicate a symmetry around Re(s)=1/2, but this is odd....
In https://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/fnleqn.htm the equation
ζ(s)=ζ(1-s) is used, where ζ is the Riemann zeta function, which I find curious, for the following reasons
this indicates a symmetry around Re(s)=1/2, which seems to be what the diagram at 20:27 of seems to imply, but contradicting the statement " The Riemann zeta function is not symmetric along with any vertical line at all " from https://www.quora.com/Is-the-Riemann-zeta-function-symmetrical
as well as the elementary consideration that on the real axis there are the trivial zeros in the negative reals that have no corresponding zeros in the positive-real-part side.
(Note that I am not asking about the symmetry ζ(s)=ζ(s*), which is more reasonable.)
What am I missing? Thanks in advance for your patience; I presume this question has been asked many times before (although I couldn't find a good answer with my Internet search).
ζ(s)=ζ(1-s) is used, where ζ is the Riemann zeta function, which I find curious, for the following reasons
this indicates a symmetry around Re(s)=1/2, which seems to be what the diagram at 20:27 of seems to imply, but contradicting the statement " The Riemann zeta function is not symmetric along with any vertical line at all " from https://www.quora.com/Is-the-Riemann-zeta-function-symmetrical
as well as the elementary consideration that on the real axis there are the trivial zeros in the negative reals that have no corresponding zeros in the positive-real-part side.
(Note that I am not asking about the symmetry ζ(s)=ζ(s*), which is more reasonable.)
What am I missing? Thanks in advance for your patience; I presume this question has been asked many times before (although I couldn't find a good answer with my Internet search).