In two dimensions, Gallagher's theorem is a strengthening of the Littlewood conjecture that holds for almost all pairs of real numbers. We prove an inhomogeneous fibre version of Gallagher's theorem, sharpening and making unconditional a result recently obtained conditionally by Beresnevich, Haynes and Velani. The idea is to find large generalised arithmetic progressions within inhomogeneous Bohr sets, extending a construction given by Tao. This precise structure enables us to verify the hypotheses of the Duffin--Schaeffer theorem for the problem at hand, via the geometry of numbers
Let be a real number. For a function , define to be the set of such that for infinitely many...
AbstractDe Mathan [B. de Mathan, Approximations diophantiennes dans un corps local, Bull. Soc. Math....
The use of Hausdorff measures and dimension in the theory of Diophantine approximation dates back to...
In two dimensions, Gallagher’s theorem is a strengthening of the Littlewood conjecture that holds fo...
Gallagher's theorem is a sharpening and extension of the Littlewood conjecture that holds for almost...
Gallagher's theorem describes the multiplicative diophantine approximation rate of a typical vector....
In two dimensions, Gallagher's theorem is a strengthening of the Littlewood conjecture that holds fo...
In two dimensions, Gallagher’s theorem is a strengthening of the Littlewood conjecture that holds fo...
In two dimensions, Gallagher’s theorem is a strengthening of the Littlewood conjecture that holds fo...
AbstractLet p be a prime number. The p-adic case of the Mixed Littlewood Conjecture states that limi...
We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensio...
Gallagher’s theorem is a sharpening and extension of the Littlewood conjecture that holds for almost...
Gallagher’s theorem is a sharpening and extension of the Littlewood conjecture that holds for almost...
Let Q be an infinite set of positive integers. Denote by W(Q) the set of n-tuples of real numbers si...
The Littlewood Conjecture in Diophantine approximation can be thought of as a problem about covering...
Let be a real number. For a function , define to be the set of such that for infinitely many...
AbstractDe Mathan [B. de Mathan, Approximations diophantiennes dans un corps local, Bull. Soc. Math....
The use of Hausdorff measures and dimension in the theory of Diophantine approximation dates back to...
In two dimensions, Gallagher’s theorem is a strengthening of the Littlewood conjecture that holds fo...
Gallagher's theorem is a sharpening and extension of the Littlewood conjecture that holds for almost...
Gallagher's theorem describes the multiplicative diophantine approximation rate of a typical vector....
In two dimensions, Gallagher's theorem is a strengthening of the Littlewood conjecture that holds fo...
In two dimensions, Gallagher’s theorem is a strengthening of the Littlewood conjecture that holds fo...
In two dimensions, Gallagher’s theorem is a strengthening of the Littlewood conjecture that holds fo...
AbstractLet p be a prime number. The p-adic case of the Mixed Littlewood Conjecture states that limi...
We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensio...
Gallagher’s theorem is a sharpening and extension of the Littlewood conjecture that holds for almost...
Gallagher’s theorem is a sharpening and extension of the Littlewood conjecture that holds for almost...
Let Q be an infinite set of positive integers. Denote by W(Q) the set of n-tuples of real numbers si...
The Littlewood Conjecture in Diophantine approximation can be thought of as a problem about covering...
Let be a real number. For a function , define to be the set of such that for infinitely many...
AbstractDe Mathan [B. de Mathan, Approximations diophantiennes dans un corps local, Bull. Soc. Math....
The use of Hausdorff measures and dimension in the theory of Diophantine approximation dates back to...