Moments de la fonction Delta de Hooley associée à un caractère
Volume 198 / 2021
Acta Arithmetica 198 (2021), 359-375
MSC: Primary 11N37, 11L40, 11N56; Secondary 11D45.
DOI: 10.4064/aa200326-11-1
Published online: 22 March 2021
Abstract
Let $f$ be an arithmetic function, $V\geq 1$ a real number and $$\Delta _V(n,f):=\sup \limits _{\substack {u \in \mathbb {R}\\ v \in [0,V]}}{\Big |\sum \limits _{\substack {d\mid n \\ \operatorname{e} ^{u} \lt d\leq \operatorname{e} ^{u+v}}}{f(d)}\Big |}. $$ 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 dependence on $V$ and including the case of complex characters.
