J. Verwee:

"Théorèmes d´Erdös-Wintner effectifs";

Betreuer/in(nen), Begutachter/in(nen): M. Drmota, G. Tenenbaum, P. Grabner, B. Martin; Institut für Diskrete Mathematik und Geometrie, 2020; Rigorosum: 20.11.2020.

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 therefore

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 eld.

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 e ective versions of the above theorems.

Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.