I was wondering if there was a name for this function:
$$G(n,k)=\sum_{j=0}^{n-1}w_n^{jk}$$
for $n,k\in\mathbb{N}$, and where
$$w_n=e^{2i\pi/n}$$
In the case that $k$ is not a multiple of $n$, we have that $G(n,k)=0$. But if $k$ is a multiple of $n$, say $k=an$, then $G(n,an)=a$. I know its a finite geometric series, but I was wondering if had a reference associated with it.
It appears to be in the form of the discrete Fourier transform of a constant. I don't know if there is a special name for the case shown above, but you might find some clues based in the Fourier transform references: https://en.wikipedia.org/wiki/Discrete_Fourier_transform etc. I hope this helps.