A. Vatwani

collaborators

3 papers

math.NT2026

Equivalence between the Functional Equation and Vorono\"Ä±-type summation identities for a class of $L$ -Functions

Arindam Roy, Jagannath Sahoo, Akshaa Vatwani

To date, the best methods for estimating the growth of mean values of arithmetic functions rely on the Vorono\"Ä± summation formula. By noticing a general pattern in the proof of h…

math.NT2025

Voronoi summation formula for the generalized divisor function $I ¨ _{z}^{(k)} (n)$

Atul Dixit, Bibekananda Maji, Akshaa Vatwani

For a fixed $z \in C$ and a fixed $k \in N$ , let $I ¨ _{z}^{(k)} (n)$ denote the sum of $z$ -th powers of those divisors $d$ of $n$ whose $k$ -th powers also divide $n$ . T…

math.NT2025

On the Second Hardy-Littlewood Conjecture

Bittu Chahal, Ertan Elma, Nic Fellini +2

The second Hardy-Littlewood conjecture asserts that the prime counting function $I ¨ (x)$ satisfies the subadditive inequality \begin{align*} Ï(x+y)\leqslant Ï(x)+Ï(y) \end{align*…

Equivalence between the Functional Equation and Vorono\"Ä±-type summation identities for a class of L-Functions

Voronoi summation formula for the generalized divisor function I¨z(k)​(n)

On the Second Hardy-Littlewood Conjecture

Equivalence between the Functional Equation and Vorono\"Ä±-type summation identities for a class of $L$ -Functions

Voronoi summation formula for the generalized divisor function $I ¨ _{z}^{(k)} (n)$