- #1
rman144
- 35
- 0
I was doing some work with the zeta function and have a question.
I am aware that the Riemann Hypothesis claims that all of the critical zeros of the analytically continued zeta function have a real part Re(z)=1/2.
My question is, does the concept apply only to the complex zeros, or the imaginary and real parts separately.
Basically, is it possible to have:
Im(zeta(z))=0
Without having:
Re(zeta(z))=0
Or does a zero of one part automatically illustrate the existence of a zero for the other?
I am aware that the Riemann Hypothesis claims that all of the critical zeros of the analytically continued zeta function have a real part Re(z)=1/2.
My question is, does the concept apply only to the complex zeros, or the imaginary and real parts separately.
Basically, is it possible to have:
Im(zeta(z))=0
Without having:
Re(zeta(z))=0
Or does a zero of one part automatically illustrate the existence of a zero for the other?