This is a long shot, but ...

The fraction of $\mathbb{Z}^2$ lattice points visible from the origin $1/\zeta(2)=6/\pi^2 \approx 61$%. The fraction of $\mathbb{Z}^3$ lattice points visible from the origin is $1/\zeta(3) \approx 83$%. And this generalizes to arbitrary dimensions $1/\zeta(d)$.

Q. Is there some geometric/visibility interpretation of a zero of $\zeta(s)$ on the critical line, $\mbox{Re}(s)=1/2$?

I suspect not, but there are various notions of fractional dimension and complex dimension that might allow $\zeta(s)$ to have a type of geometric interpretation in dimension $s$...?

This is a long shot, but ...

The fraction of $\mathbb{Z}^2$ lattice points visible from the origin $1/\zeta(2)=6/\pi^2 \approx 61$%. The fraction of $\mathbb{Z}^3$ lattice points visible from the origin is $1/\zeta(3) \approx 83$%. And this generalizes to arbitrary dimensions $1/\zeta(d)$.

Q. Is there some geometric/visibility interpretation of a zero of $\zeta(s)$ on the critical line, $\mbox{Re}(s)=1/2$?

I suspect not, but there are various notions of fractional dimension and complex dimension that might allow $\zeta(s)$ to have a type of geometric interpretation in dimension $s$...?

This is a long shot, but ...

The fraction of $\mathbb{Z}^2$ lattice points visible from the origin $1/\zeta(2)=6/\pi^2 \approx 61$%. The fraction of $\mathbb{Z}^3$ lattice points visible from the origin is $1/\zeta(3) \approx 83$%. And this generalizes to arbitrary dimensions $1/\zeta(d)$.

Q. Is there some geometric/visibility interpretation of a zero of $\zeta(s)$ on the critical line, $\mbox{Re}(s)=1/2$?

I suspect not, but there are various notions of complex dimension that might allow $\zeta(s)$ to have a type of geometric interpretation in dimension $s$...?

This is a long shot, but ...

The fraction of $\mathbb{Z}^2$ lattice points visible from the origin $1/\zeta(2)=6/\pi^2 \approx 61$%. The fraction of $\mathbb{Z}^3$ lattice points visible from the origin is $1/\zeta(3) \approx 83$%. And this generalizes to arbitrary dimensions $1/\zeta(d)$.

Q. Is there some geometric/visibility interpretation of a zero of $\zeta(s)$ on the critical line, $\mbox{Re}(s)=1/2$?

I suspect not, but there are various notions of fractional dimension and complex dimension that might allow $\zeta(s)$ to have a type of geometric interpretation in dimension $s$...?