Let the "Simple Zeros Conjecture (SZC)" be the statement that all zeros of the Riemann zeta function are simple.

I have often heard of the statement that the SZC is stronger than the Riemann Hypothesis (RH). However, I have never seen or heard of any justification of this claim, and a quick internet search doesn't seem to reveal any result like SZC $\implies$ RH.

Therefore, can someone explain why the SZC is said to be stronger than the RH ?

withoutRH. $\endgroup$ – Peter Humphries Jun 1 at 20:034more comments