# Effectiveness of the implied constant in an inequality

A result of Heath-Brown states: For $$a_1,...,a_n$$ be arbitrary complex numbers, $$\sideset{}{^*}\sum_{m\le M} \left|\sideset{}{^*}\sum_{n\le M}a_n\left(\frac{n}{m}\right)\right|^{2} \ll_{\epsilon}(MN)^{\epsilon}(M+N)\sideset{}{^*}\sum_{n\le N}|a_n|^2$$ $$\sideset{}{^*}\sum$$ indicates restriction to odd square free values.

Is the implied constant effective ?

• Do you want to give a specific reference to this result? – Greg Martin Apr 8 at 17:16