Leírás
Online Number Theory Seminar
Abstract: A $q$-ary sum-of-digits function $s_q$ is defined as $s_q(n)=\sum_{j\geq0} \varepsilon_j$, where $\varepsilon_j$ are the digits in the $q$-ary digital expansion of $n$. Sum-of-digits function also serve as an important prototype of the $q$-additive functions. Besides their various asymptotic distribution and arithmetic properties, $q$-ary sum-of-digits functions or their weighted variants $s_{q,\gamma}$ covers some basic sequences playing important role in the uniform distribution theory mod 1. In 2007 F.Pillichshammer proved a criterion when sequences generated by the weighted sum-of-digits function are uniformly distributed mod 1. In the talk we shall discuss some basic characteristics of the asymptotic distribution of sum-of-digits and $q$-additive functions, as well as their connections to the mention Pillichshammer's criterion (this part of the talk is based on the joint work with L. Mišík and O.Strauch).
For access please contact the organizers (ntrg[at]science.unideb.hu).