zeta distribution

For infinite and it becomes a Zeta distribution.

Indeed the terms "Zipf distribution" and the "zeta distribution" are often used interchangeably.

Some remarks on the Riemann zeta distribution by Allan Gut.

In probability theory and statistics, the zeta distribution is a discrete probability distribution.

Indeed, Zipf's law is sometimes synonymous with "zeta distribution," since probability distributions are sometimes called "laws".

Zipf's law, also sometimes called the zeta distribution, may be thought of as a discrete counterpart of the Pareto distribution.

Zeta distribution (discrete)

André Weil rewrote Tate's thesis in this language, characterizing the zeta distribution on the idele group; and has also applied it to the explicit formula of an L-function.

What Gut calls the Riemann zeta distribution is actually the probability distribution of log X, where X is a random variable with what this article calls the zeta distribution.