arXiv subjects

A. Sankaranarayanan

Publications and source records attributed to A. Sankaranarayanan.

3 recordsLinked to original sources

arXiv2026

On the discrete mean square of certain hybrid sum involving $a_{\mathbb{K}}(n)$

Let $\mathbb{K}$ be a non-normal algebraic number field of cubic degree given by the polynomial $x^{3}+ax^{2}+bx+c$ of discriminant $D_{\mathbb{K}}<0$. For sufficiently large $x$, we establish an asymptotic formula for the hybrid sum $$\sum\limits_{\substack{n= \sum_{i=1}^{8}n_{i}^{2}\leq x\\ (n_{1},n_{2},n_{3},n_{4},n_{5},n_{6},n_{7},n_{8})\in \mathbb{Z}^{8} }} a_{\mathbb{K}}^{2}(n)$$ with a tight error term.

math.NT↗

arXiv2025

On the distribution of the strongly multiplicative function $2^{\omega(n)}$ on the set of natural numbers

In this paper, we study the distribution of the sequence of integers $2^{\omega(n)}$ under the assumption of the strong Riemann hypothesis, where $\omega(n)$ denotes the number of distinct prime divisors of $n$. We provide an asymptotic formula for the sum $\displaystyle\sum_{n\leq x}2^{\omega(n)}$ under this assumption. We study the sum $\displaystyle\sum_{n\leq x}2^{\omega(n)}$ unconditionally too.

math.NT↗

arXiv2023

On certain kernel functions and shifted convolution sums of the Fourier coefficients

We study the behavior of the shifted convolution sum involving fourth power of the Fourier coefficients of holomorphic cusp forms with a weight function to be the $k$-full kernel function for any fixed integer $k\geq2$.

math.NT↗