I'm studying Davenport's proof of Dirichlet Class Number Theorem and I'm having troubles with this statement:
Consider the sum
$$\sum_{m_1 m_2<N; (m_1,m_2,d)=1} \left(\frac{d}{m_1}\right)= \sum_{m_1 <\sqrt{N}} \left(\frac{d}{m_1}\right) \sum_{m_2 <N/m_1} 1 + ... $$
then $\sum_{m_2 <N/m_1} 1 = \frac{N}{m_1}\frac{\phi(|d|}{|d|}+O(\phi(|d|)$
I've tried to solve it by using the orthogonal relations of Dirichlet characters but I didn't succeed. Any ideas?