Digital expansion of exponential sequences

Michael Fuchs*

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We consider the q-axy digital expansion of the first N terms of an exponential sequence an. Using a result due to Kiss and Tichy [8], we prove that the average number of occurrences of an arbitrary digital block in the last c log N digits is asymptotically equal to the expected value. Under stronger assumptions we get a similar result for the first (formula presented) digits, where ε is a positive constant. In both methods, we use estimations of exponential sums and the concept of discrepancy of real sequences modulo 1 plays an important role.

Original languageEnglish
Pages (from-to)477-487
Number of pages11
JournalJournal de Theorie des Nombres de Bordeaux
Volume14
Issue number2
DOIs
StatePublished - 1 Jan 2002

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