I've been doing research in information theory that had some superficial connections to the Zeta function, since I was making use of logarithms of complex numbers.
In short, we'd be looking at the Zeta function using values of s produced by powers of the logarithm function:
I noticed several zeros for n = 6:
But, I don't know enough about this topic to be sure that this is actually interesting, since I know that at least some of the zeros of this function are considered "trivial". Nonetheless, I thought I'd share this in case some of you found it interesting and had insights.