Yaghoub Rahimi

activity

20182026

L_{1} / L_{2}

Minimization

77 citations · 85 across the 9 of their papers we have counts for

collaborators

10 papers

math.NT2026

Density Bounds in Hua's Theorem for Prime Squares

Michael T. Lacey, Hamed Mousavi, Yaghoub Rahimi +1

We prove a density version of Hua's theorem in the five-variable case: if $P$ is a subset of the primes with relative lower density greater than $0.82$ , then every suffici…

math.NT2026

Primes with Restricted-Digit Differences

Rui Han, Yaghoub Rahimi, Fan Yang

Fix a base $b \geq 2$ and a digit set $D \subset {0, 1, \dots, b - 1}$ , and let $C_{k}$ be the set of integers in $[0, b^{k})$ whose $k$ base- $b$ digits all lie in $\mathcal…

math.CA2026

On the small denominator problem for generalized Minkowski--Funk transforms

Rui Han, Yaghoub Rahimi

Rubin's generalized Minkowski--Funk transforms $M_{t}^{α}$ on the sphere $S^{n}$ give rise, for irrational radii $t = cos (β π)$ , to a small denominator problem governed by the asy…

math.NT2024

A Density Theorem for Higher Order Sums of Prime Numbers

Michael T. Lacey, Hamed Mousavi, Yaghoub Rahimi +1

Let $P$ be a subset of the primes of lower density strictly larger than $\frac{1}{2}$ . Then, every sufficiently large even integer is a sum of four primes from the set $P$ . We establis…

math.NT2023

Averages over the Gaussian Primes: Goldbach's Conjecture and Improving Estimates

Christina Giannitsi, Ben Krause, Michael Lacey +2

We prove versions of Goldbach conjectures for Gaussian primes in arbitrary sectors. Fix an interval $ω \subset T$ . There is an integer $N_{ω}$ , so that every odd integer $n$ …

eess.SP2022

A Lifted $ℓ_{1}$ Framework for Sparse Recovery

Yaghoub Rahimi, Sung Ha Kang, Yifei Lou

Motivated by re-weighted $ℓ_{1}$ approaches for sparse recovery, we propose a lifted $ℓ_{1}$ (LL1) regularization which is a generalized form of several popular regularizations i…

math.CA2021

Improving and Maximal Inequalities for Primes in Progressions

Christina Giannitsi, Michael T. Lacey, Hamed Mousavi +1

Assume that $y < N$ are integers, and that $(b, y) = 1$ . Define an average along the primes in a progression of diameter $y$ , given by integer $(b, y) = 1$ . \begin{align*} A_{N,y,b…

math.NT2021

Endpoint $ℓ^{r}$ improving estimates for Prime averages

Michael T. Lacey, Hamed Mousavi, Yaghoub Rahimi

Let $Λ$ denote von Mangoldt's function, and consider the averages \begin{align*} A_N f (x) &=\frac{1}{N}\sum_{1\leq n \leq N}f(x-n)Λ(n) . \end{align*} We prove sharp $ℓ^{p}$ -…

math.NA2019★ 77 cited

Accelerated Schemes for the $L_{1} / L_{2}$ Minimization

Chao Wang, Ming Yan, Yaghoub Rahimi +1

In this paper, we consider the $L_{1} / L_{2}$ minimization for sparse recovery and study its relationship with the $L_{1}$ - $α L_{2}$ model. Based on this relationship, we propose three nu…

math.NA2018★ 8 cited

A Scale Invariant Approach for Sparse Signal Recovery

Yaghoub Rahimi, Chao Wang, Hongbo Dong +1

In this paper, we study the ratio of the $L_{1}$ and $L_{2}$ norms, denoted as $L_{1} / L_{2}$ , to promote sparsity. Due to the non-convexity and non-linearity, there has been little atten…