Combinatorical and Algebraic Structures Seminar
Session details
Date: | 2.10.2012 |
Speaker: | Wolfgang Steiner, LIAFA, Université Paris VII |
Title: | Patterns in rational base number systems |
Abstract: | (spoluautoři: Johannes Morgenbesser and Jörg Thuswaldner) Akiyama, Frougny, and Sakarovitch recently introduced number systems with a rational number as base. They established relations to Mahler's 3/2-problem as well as the Josephus problem. We show that the patterns of digits in the expansions of positive integers are uniformly distributed in these number systems. We study the sum-of-digits function of number systems with rational base p/q and use expansions w.r.t. this base to construct normal numbers in base p in the spirit of Champernowne. In the proofs we use self-affine tiles that are defined in certain subrings of the adele ring. |
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