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.

On the interval $[0,1)\cup(1,\infty]$ it is one to one. – Simply Beautiful Art Jul 29 '17 at 23:08 — Simply Beautiful Art, Jul 29 '17 at 23:08

score 5 · Answer 1 · answered Jul 29 '17 at 23:04

5

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 $1/2$.

answered Jul 29 '17 at 23:04

Tai

2,235

what about at t = t* where a zero occurs and 0 < sigma <= 1/2? – Hass Jul 30 '17 at 13:36

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

1 Answers1