18 citations · 29 across the 12 of their papers we have counts for
5 papers · 1 filter
Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces
Jean Bourgain
Using the multilinear theory of oscillatory integral operators, we establish a square function inequality with implications to moment inequalities for discrete exponential sums whi…
On representation of integers by binary quadratic forms
J. Bourgain, E. Fuchs
Given a negative , we give a new upper bound on the number of square free integers which are represented by some but not all forms of the genus of a pr…
Distribution of Elements of Cosets of Small Subgroups and Applications
Jean Bourgain, Sergei V. Konyagin, Igor E. Shparlinski
We obtain a series of estimates on the number of small integers and small order Farey fractions which belong to a given coset of a subgroup of order of the group of units of th…
Distribution on elements of cosets of small subgroups and applications
Jean Bourgain, Sergei Konyagin, Igor Shparlinski
We obtain a series of estimates on the number of small integers and small order Farey fractions which belong to a given coset of a subgroup of order of the group of units of th…
On the Furstenberg measure and density of states for the Anderson-Bernoulli model at small disorder
Jean Bourgain
We establish new results on the dimension of density of states for the Anderson-Bernoulli model at small disorder