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Théorèmes d'Erdös-Wintner effectifs

Abstract : Natural integers lend themselves to multiple forms of representation. Among the most fundamental are prime factors decomposition and representation in a numeral system. The literature has there- fore naturally been interested in associated morphisms, that is, arithmetic functions that respect the underlying structures. Additive functions transport the multiplicative structure of N∗ to the additive structure of C; additive q-additive functions transport the q-adic representation to this same additive structure of the complex number field. The famous Erd˝os-Wintner theorem provides a complete answer to the question of the existence of a limit distribution law for additive functions. Analogous statements have been established for other representation systems, such as q-adic or Cantor representations. A partial version is known for the representation in the Zeckendorf base. In this work we propose on the one hand to complete this last statement and, on the other hand, to establish effective versions of the above theorems.
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Submitted on : Monday, March 22, 2021 - 11:35:44 AM
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Johann Verwee. Théorèmes d'Erdös-Wintner effectifs. Mathématiques [math]. Université de Lorraine; Technische Universität (Vienne), 2020. Français. ⟨NNT : 2020LORR0180⟩. ⟨tel-03176266⟩



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