Ataleshvara Bhargava

activity

20212026

collaborators

6 papers

math.NT2026

An Approximate Version of Vu's Theorem on Economical Subbases For Non-Integer Exponents

Ataleshvara Bhargava

We prove an approximate analog of Vu's Theorem on economical bases of $k$ th powers for non-integer powers. Fix a non-integer $θ > 2$ and real $τ > 0$ . Let $s \geq θ^{2} + 9 θ^{3/2} + 2$ if…

math.NT2026

Mean Value Estimates for a Real-Exponent Analogue of Waring's Problem

Ataleshvara Bhargava

For non-integer $θ > 3$ and $κ \geq 1$ , we show that the smallest $r_{0}$ such that the mean value estimate \[ \int_{-κ}^κ \Big| \sum_{X < x \leq 2X} e(αx^θ) \Big|^{2r} dα\ll_ε κX^{2r…

math.NT2026

Sharp Transitions for Localized Solutions to a Diophantine Inequality

Ataleshvara Bhargava

For fixed $τ > 0$ , non-integer $θ > 2$ and large enough $s$ , we investigate the number of solutions to the Diophantine inequality $∣ x_{1}^{θ} + \dots + x_{s}^{θ} - R ∣ < τ$ as $R \to \infty$ . H…

math.AP2025

Intermittent singular solutions of the stationary 2D Navier-Stokes equations in sharp Sobolev spaces

Estepan Ashkarian, Ataleshvara Bhargava, Nicholas Gismondi +1

In this paper we construct non-trivial solutions to the stationary Navier-Stokes equations on the two dimensional torus which lie in $\bigcap_{ε\in (0,1)} L^{2-ε}(\mathbb{T}^2) \ca…

math.CA2024

A study guide for the $ℓ^{2}$ decoupling theorem for the paraboloid

Ataleshvara Bhargava, Tiklung Chan, Zi Li Lim +1

This article serves as a study guide for the $ℓ^{2}$ decoupling theorem for the paraboloid originally proved by Bourgain and Demeter. Given its popularity and importance, many exp…

math.CO2021

The Rank of the Sandpile Group of Random Directed Bipartite Graphs

Atal Bhargava, Jack DePascale, Jake Koenig

We identify the asymptotic distribution of $p$ -rank of the sandpile group of a random directed bipartite graphs which are not too imbalanced. We show this matches exactly that of t…

An Approximate Version of Vu's Theorem on Economical Subbases For Non-Integer Exponents

Mean Value Estimates for a Real-Exponent Analogue of Waring's Problem

Sharp Transitions for Localized Solutions to a Diophantine Inequality

Intermittent singular solutions of the stationary 2D Navier-Stokes equations in sharp Sobolev spaces

A study guide for the ℓ2 decoupling theorem for the paraboloid

The Rank of the Sandpile Group of Random Directed Bipartite Graphs

A study guide for the $ℓ^{2}$ decoupling theorem for the paraboloid