When replacing the circle group with the dyadic group of integers, the Riemann zeta function becomes an explicit entire function for which all roots are on the imaginary axes. This is the Dyadic Riemann Hypothesis.
One of the attempts to quantize space without losing too much symmetry is ergodic theory. Much of my thesis belongs to this program. It is a flavor of quantum calculus, as “no limits” are involved. The story is closely related to Jacob Feldman, one of my heroes of my graduate and postdoc time. I write this blog entry after having … ….