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arXiv · 2608.13172

On $\mathcal{B}^4$-almost periodicity for a class of arithmetical functions

Kritika Aggarwal·Debika Banerjee·Shubham Gupta
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Abstract

In this paper, we establish the $\mathcal{B}^4$-almost periodicity in the sense of Besicovitch for a suitably normalized error term associated with a broad class of arithmetical functions introduced by Chandrasekharan and Narasimhan. This result significantly strengthens $\mathcal{B}^2$-almost periodicity previously investigated in the literature for related error terms. By deriving truncated Vorono\"{i}-type formulas, we demonstrate that the normalized error term lies in the Besicovitch space $B^4$. As a consequence, we deduce that the error term admits a limit probability distribution and establish an explicit formula for its mean fourth power moment.

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Kritika Aggarwal, Debika Banerjee, Shubham Gupta. 2026-08-13. On $\mathcal{B}^4$-almost periodicity for a class of arithmetical functions. https://arxiv.org/abs/2608.13172

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