Moments de la fonction Delta de Hooley associée à un caractère

Abstract

Let $f$ be an arithmetic function, $V⩾1$ a real number and $${\Delta }_V(n,f):=\underset{\begin{array}{c}u\in \mathbb{R}\\ v\in [0,V]\end{array}}{\sup }|\sum _{\begin{array}{c}d\mid n\\ {\mathrm{e}}^u<d⩽{\mathrm{e}}^{u+v}\end{array}}f(d)|.$$ In a paper published in 2012, La Bretèche and Tenenbaum investigated weighted moments of ${\Delta }_1(n,f)$ where $f$ is a non principal real Dirichlet character, or the Möbius function. Answering a question of Hooley, we extend their results studying dependance in $V$ and including the case of complex characters.

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