A. Vatwani

activity

20182026

L

-functions in the Selberg class

1 citations · 1 across the 6 of their papers we have counts for

collaborators

8 papers

math.NT2026

Equivalence between the Functional Equation and Vorono\"ı-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\"ı summation formula. By noticing a general pattern in the proof of hi…

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 $π (x)$ satisfies the subadditive inequality \begin{align*} π(x+y)\leqslant π(x)+π(y) \end{align*} fo…

math.NT2023

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

Atul Dixit, Bibekananda Maji, Akshaa Vatwani

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

math.NT2022★ 1 cited

Riesz type criteria for $L$ -functions in the Selberg class

Shivajee Gupta, Akshaa Vatwani

We formulate a generalization of Riesz-type criteria in the setting of $L$ -functions belonging to the Selberg class. We obtain a criterion which is sufficient for the Grand Riemann…

math.NT2022

A modular relation involving non-trivial zeros of the Dedekind zeta function, and the Generalized Riemann Hypothesis

Atul Dixit, Shivajee Gupta, Akshaa Vatwani

We give a number field analogue of a result of Ramanujan, Hardy and Littlewood, thereby obtaining a modular relation involving the non-trivial zeros of the Dedekind zeta function.…

math.NT2020

Joint Extreme values of $L$ -functions

Kamalakshya Mahatab, Łukasz Pańkowski, Akshaa Vatwani

We consider $L$ -functions $L_{1}, \dots, L_{k}$ from the Selberg class which have polynomial Euler product and satisfy Selberg's orthonormality condition. We show that on every vertical…

math.NT2019

Zeros of Dirichlet polynomials

Arindam Roy, Akshaa Vatwani

We consider a certain class of multiplicative functions $f : N \to C$ and study the distribution of zeros of Dirichlet polynomials $F_N(s)= \sum_{n\le N} f(n…

math.NT2018

Zeros of partial sums of $L$ -functions

Arindam Roy, Akshaa Vatwani

We consider a certain class of multiplicative functions $f : N \to C$ . Let $F (s) = \sum_{n = 1}^{\infty} f (n) n^{- s}$ be the associated Dirichlet series and $F_N(s…

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

On the Second Hardy-Littlewood Conjecture

Voronoi summation formula for the generalized divisor function σz(k)​(n)

Riesz type criteria for L-functions in the Selberg class