Is the Riemann Zeta function a one-to-one function?

Question

I Couldn't find any reference or a way to show whether the Riemann Zeta function is a one-to one function. Any references or proof/disproof of this property would be enlightening.

Answer 1

The Riemann zeta function has many zeros, so it is not one-to-one. The Riemann hypothesis is all about showing that the only zeros of the Riemann zeta function are the negative even integers and complex numbers with real part $1/2$.