Let $\chi_{-4}$ be the Dirichlet character defined by $$ \chi_{-4}(m) = \begin{cases} 1, & m\equiv 1 \mod 4 \\ -1, &m \equiv 3 \mod 4\\ 0, &m \equiv 0 \mod 2.\end{cases}$$ I know that $$r_2(n)=4\sum_{d|n} \chi_{-4}(d)$$ counts the number of ways one can write $n$ as a sum of two squares. This got me curious as to what $$\sum_{p|n} \chi_{-4}(p)$$ (p is prime) counts? Im looking for a quick reference or explanation. Thanks!
2026-02-23 07:17:06.1771831026
What does $\sum_{p|n} \chi_{-4}(p)$ count?
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