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arXiv · 2610.41658

Estimates of Lucas series and expansions in non-integer bases

Vilmos Komornik·Marco Pedicini
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Abstract

Special Fibonacci and Lucas type expansions proved useful to ``correct'' some theorems on the number of expansions in non-integer bases \cite{BaiKomLor2021, KomLorPed2024, KomLorPed2025}. The proof of a key lemma was non-constructive. It was made constructive in the Fibonacci case by giving a precise estimate of the growth of the partial sums of the series of the inverses of the Fibonacci numbers \cite{KomPed2025}. In this paper we extend this result to the general case.

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Vilmos Komornik, Marco Pedicini. 2026-10-30. Estimates of Lucas series and expansions in non-integer bases. https://arxiv.org/abs/2610.41658

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