Some news on bilinear decomposition of the Möbius function
Appears in collection : Prime numbers : new perspectives / Nombres premiers : nouvelles perspectives
This talk presents some news on bilinear decompositions of the Möbius function. In particular, we will exhibit a family of such decompositions inherited from Motohashi's proof of the Hoheisel Theorem that leads to $\sum_{n\leq X,(n,q)=1) }^{} \mu (n)e(na/q)\ll X\sqrt{q}/\varphi (q)$ for $q \leq X^{1/5}$ and any $a$ prime to $q$.
