It doesn’t change if you apply it to complex arguments does it?

Zeta(z) = 1 + 1/2^z + 1/3^z + …

Where z in C.

In fact, I thought that was why it’s called the Riemann zeta function. Euler applied it to an integer whereas Riemann applied it to complex arguments.

Edit to add: my memory was correct. Reimann extended Euler’s definition to all complex s not equal to 1. https://en.wikipedia.org/wiki/On_the_Number_of_Primes_Less_T...