Borwein–Choi conjecture on representations by binary quadratic forms

Let $N$ be a squarefree positive integer, and let $r_{2,N}(n)$ denote the number of representations of $n$ by $x^2+Ny^2$, counting signs and order. Then

Borwein–Choi conjecture.

$$\sum_{n \le x} {r_{2,N}(n)}^2 \sim \frac{3}{N} \Big( \prod_{p|2N} \frac{2p}{p+1} \Big ) x\log x.$$

The conjecture concerns the mean square of representation numbers for the positive definite binary quadratic form $x^2+Ny^2$. The paper's abstract states that it proves the remaining case of this conjecture, so the conjecture is resolved.