On the representation of an integer in Ostrowski and recurrence numeration systems

2024/09/10 by Mittal, Mohit, Divyum Sharma, Sharma, Divyum
Computer Science · Mathematics · #11A63 #11D61 #11J86 #11R04 #11R11 #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #Number Theory (math.NT) #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.2409.06232

openalex publication_date 2024/09/10 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28

Abstract

We provide an effective upper bound for positive integers with bounded Hamming weights with respect to both a linear recurrence numeration system and an Ostrowski-α numeration system, where α is a quadratic irrational. We prove a similar result for the representation of an integer in two different Ostrowski numeration systems.

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