Abschätzung der Hausdorffdimension für Mengen mit vorgeschriebenen Häufigkeiten der Ziffern.
We prove a local analogue of a theorem of J. Martinet about the absolute norm of the relative discriminant ideal of an extension of number fields. The result can be seen as a statement about -primary units. We also prove a similar statement about the absolute norms of -primary units, for all primes .
For abstract numeration systems built on exponential regular languages (including those coming from substitutions), we show that the set of real numbers having an ultimately periodic representation is if the dominating eigenvalue of the automaton accepting the language is a Pisot number. Moreover, if is neither a Pisot nor a Salem number, then there exist points in which do not have any ultimately periodic representation.