Note on the Riemann Zeta Function

As you know, I’ve been doing research in information theory, and some of my recent work has some superficial connections to the Zeta function, since I was making use of logarithms of complex numbers.

I noticed the following graph:

In short, we’d be looking at the Zeta function using values of s produced by powers of the logarithm function:

$zeta(log^n (-1) /x).$

There appears to be several zeros for n = 6.

You can see it yourself on wolfram using the following link:

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.

Regards,

Charles