Prasuna Bandi

activity

20192026

most citedHausdorff dimension and exact approximation order in

R^{n}

2 citations · 5 across the 8 of their papers we have counts for

collaborators

8 papers

math.NT2026

Averaged Fourier Estimates and Dyadic Approximation on the Cantor set

Prasuna Bandi

Let $C$ be the middle-third Cantor set and let $μ$ be the natural Cantor probability measure. Let \[ γ=\frac{\log2}{\log3}. \] The two main results of this paper are \[ μ\{x\in C:\…

math.NT2026

On the Hausdorff Dimension of weighted exactly Approximable Vectors

Prasuna Bandi, Reynold Fregoli

We show that the Hausdorff dimension of $w$ -weighted $τ$ -exactly approximable vectors in $R^{d}$ coincides with the Hausdorff dimension of $w$ -weighte…

math.NT2025

Submanifold-genericity of $R^{d}$ -actions and uniform multiplicative Diophantine approximation

Prasuna Bandi, Reynold Fregoli, Dmitry Kleinbock

In this paper, we prove a new ergodic theorem for $R^{d}$ -actions involving averages over dilated submanifolds, thereby generalizing the theory of spherical averages. Our ma…

math.NT2023★ 2 cited

Hausdorff dimension and exact approximation order in $R^{n}$

Prasuna Bandi, Nicolas de Saxcé

Given a non-increasing function $ψ : N \to R^{+}$ such that $s^{\frac{n + 1}{n}} ψ (s)$ tends to zero as $s$ goes to infinity, we show that the set of points in $\math…

math.NT2022★ 1 cited

Exact approximation order and well-distributed sets

Prasuna Bandi, Anish Ghosh, Debanjan Nandi

We prove that for any proper metric space $X$ and a function $ψ : (0, \infty) \to (0, \infty)$ from a suitable class of approximation functions, the Hausdorff dimensions of the set $W_ψ(…

math.NT2020★ 1 cited

Small solutions of quadratic forms with congruence conditions

Prasuna Bandi, Anish Ghosh

We consider a system of homogeneous quadratic forms with congruence conditions in $n \geq 3$ variables and prove the existence of two linearly independent integral solutions of boun…

math.NT2020★ 1 cited

A generic effective Oppenheim theorem for systems of forms

Prasuna Bandi, Anish Ghosh, Jiyoung Han

We prove a uniform effective density theorem as well as an effective counting result for a generic system comprising a polynomial with a mild homogeneous condition and several line…

math.NT2019

On the density at integer points of a system comprising an inhomogeneous quadratic form and a linear form