Let $G$ an abelian group with $\vert G\vert<+\infty$ and $N_1, ..., N_k$ , $k$ subsets of $G$. Let $a \in G$.
We want to find $\vert \{(n_1,...,n_k)\in N_1\times...\times N_k \ / \ n_1+...+n_k=a \}\vert$.
Apparently we can use the character theory to find this number. So if someone has references on that fact, it would be great.
Thanks in advance !