Add to ORKGThe Littlewood Conjecture in Diophantine approximation can be thought of as a problem about covering the plane by a union of hyperbolas centered at rational points. In this paper we consider the problem of translating the center of each hyperbola by a random amount which depends on the denominator of the corresponding rational. Using a randomized covering argument we prove that, not only is this randomized version of the Littlewood Conjecture true for almost all choices of centers, an even stronger statement with an extra factor of a logarithm also holds
We study the extent to which divisors of a typical integer $n$ are concentrated. In particular, defi...
We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensio...
AbstractThe hive model is used to show that the saturation of any essential Horn inequality leads to...
AbstractLet p be a prime number. The p-adic case of the Mixed Littlewood Conjecture states that limi...
In two dimensions, Gallagher's theorem is a strengthening of the Littlewood conjecture that holds fo...
Let $\|x\|$ denote the distance from $x\in\mathbb{R}$ to the set of integers $\mathbb{Z}$. The Littl...
Gallagher's theorem is a sharpening and extension of the Littlewood conjecture that holds for almost...
For any given real number $\alpha$ with bounded partial quotients, we construct explicitly continuum...
For any given real number $\alpha$ with bounded partial quotients, we construct explicitly continuum...
AbstractLet hR denote an L∞ normalized Haar function adapted to a dyadic rectangle R⊂[0,1]d. We show...
In two dimensions, Gallagher’s theorem is a strengthening of the Littlewood conjecture that holds fo...
In two papers, Littlewood studied seemingly unrelated constants: (i) the best α such that for any po...
We prove a higher-rank analogue of a well-known result of W. M. Schmidt concerning almost everywhere...
AbstractWe show that the distance between en and its nearest integer is estimated below by e−cnlogn ...
Gallagher's theorem describes the multiplicative diophantine approximation rate of a typical vector....
We study the extent to which divisors of a typical integer $n$ are concentrated. In particular, defi...
We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensio...
AbstractThe hive model is used to show that the saturation of any essential Horn inequality leads to...
AbstractLet p be a prime number. The p-adic case of the Mixed Littlewood Conjecture states that limi...
In two dimensions, Gallagher's theorem is a strengthening of the Littlewood conjecture that holds fo...
Let $\|x\|$ denote the distance from $x\in\mathbb{R}$ to the set of integers $\mathbb{Z}$. The Littl...
Gallagher's theorem is a sharpening and extension of the Littlewood conjecture that holds for almost...
For any given real number $\alpha$ with bounded partial quotients, we construct explicitly continuum...
For any given real number $\alpha$ with bounded partial quotients, we construct explicitly continuum...
AbstractLet hR denote an L∞ normalized Haar function adapted to a dyadic rectangle R⊂[0,1]d. We show...
In two dimensions, Gallagher’s theorem is a strengthening of the Littlewood conjecture that holds fo...
In two papers, Littlewood studied seemingly unrelated constants: (i) the best α such that for any po...
We prove a higher-rank analogue of a well-known result of W. M. Schmidt concerning almost everywhere...
AbstractWe show that the distance between en and its nearest integer is estimated below by e−cnlogn ...
Gallagher's theorem describes the multiplicative diophantine approximation rate of a typical vector....
We study the extent to which divisors of a typical integer $n$ are concentrated. In particular, defi...
We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensio...
AbstractThe hive model is used to show that the saturation of any essential Horn inequality leads to...