Regularities of the Distribution of ß-adic van der Corput Sequences

• Autores: Wolfgang Steiner
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 149, Nº 1, 2006, págs. 67-81
• Idioma: inglés
• DOI: 10.1007/s00605-005-0370-8
• Texto completo no disponible (Saber más ...)
• Resumen

  • For Pisot numbers ß with irreducible ß-polynomial, we prove that the discrepancy function D(N, [0,y)) of the ß-adic van der Corput sequence is bounded if and only if the ß-expansion of y is finite or its tail is the same as that of the expansion of 1. If ß is a Parry number, then we can show that the discrepancy function is unbounded for all intervals of length . We give explicit formulae for the discrepancy function in terms of lengths of iterates of a reverse ß-substitution.