[zombot]

And as if all of that were not head-exploding enough, I'm still searching for an implementation of the zeta function for complex arguments...

[seanhunter]

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...

[adgjlsfhk1]

that definition only converges for Re(z)>1. for Re(z)<=1, you need alternate formulas

[seanhunter]

Yes. Riemann gives them in the paper, including derivation, it’s just a bit annoying to type/read them here because hn doesn’t support mathjaxx.

https://www.claymath.org/wp-content/uploads/2023/04/Wilkins-...

[zombot]

I'm just not mathematician enough to convert that into a C function. Let alone one that is both efficient and reasonably accurate.