Ataleshvara Bhargava

activity

20242026

collaborators

4 papers

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_{Îµ\in (0,1)} L^{2-Îµ}(\mathbb{T}^2) \…

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…

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

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