Dissertationen (eigene und begutachtete):

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.

Kurzfassung englisch:
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.