[seanhunter]

This is way above my paygrade, but trivial zeros of the zeta function are at the negative even integers (ie they are of the form s = -2n for some natural number n) because that's what Riemann said in his paper where he made the conjecture[1]

    This equation now gives the value of the function ζ(s) for all complex numbers s and shows that this function is one-valued and finite for all finite values of s with the exception of 1, and also that it is zero if s is equal to a negative even integer.

I don't think people get to retcon some other kind of zero into being trivial.

[1] https://www.claymath.org/wp-content/uploads/2023/04/Wilkins-...