On short averages of the Fibonacci partition function

We show that short averages of the Fibonacci partition function over $(H, H + H^α]$ can be significantly smaller than long averages over $(0,H]$, for any constant $α\in (0,1)$. This provides a negative answer to a question that we asked in our previous work on this topic (Journal of Number Theory, 2024).

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.39817
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

On short averages of the Fibonacci partition function

Sam Chow, Owen Jones
arXiv (Cornell University)
Analytic Number Theory Research
preprint

On short averages of the Fibonacci partition function

Sam Chow, Owen Jones
preprint en

Abstract

We show that short averages of the Fibonacci partition function over $(H, H + H^α]$ can be significantly smaller than long averages over $(0,H]$, for any constant $α\in (0,1)$. This provides a negative answer to a question that we asked in our previous work on this topic (Journal of Number Theory, 2024).

arXiv (Cornell University)
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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On short averages of the Fibonacci partition function — Sam Chow, Owen Jones · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS