Kritika Aggarwal | Searcharxiv

arXiv2026

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

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.

math.NT↗

arXiv2025

A weighted divisor problem and exponential sum

In this paper, we investigate a weighted divisor problem involving the exponential sum of $D_{(1)}(n)$, the $n$th coefficient in the Dirichlet series expansion of $\zeta'(s)^2$. We establish a truncated Vorono\"{i} type formula for the error term of $\sum_{n\leq x}D_{(1)}(n)e(nh/k)$, analogous to the results obtained by Jutila. Utilizing this truncated formula, we derive a mean square estimate of the error term. In addition, we study the associated Riesz sum and the corresponding error term, along with its mean square estimate.

math.NT↗