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Moments de la fonction Delta de Hooley associée à un caractère

Volume 198 / 2021

Alexandre Lartaux Acta Arithmetica 198 (2021), 359-375 MSC: Primary 11N37, 11L40, 11N56; Secondary 11D45. DOI: 10.4064/aa200326-11-1 Published online: 22 March 2021


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.


  • Alexandre LartauxUniversité de Paris, Sorbonne Université
    CNRS Institut de Mathématiques de Jussieu – Paris Rive Gauche
    F-75013 Paris, France

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