180 citations · 947 across the 92 of their papers we have counts for
49 papers · 1 filter
On the number of th powers inside arithmetic progressions
Jean Bourgain, Ciprian Demeter
We find upper bounds that are sharp for the number of th powers inside arbitrary arithmetic progressions whose step has many divisors.
Three applications of the Siegel mass formula
Jean Bourgain, Ciprian Demeter
We present three applications of the Siegel mass formula. First we estimate the number of solutions of a quadratic system of equations. We also include estimates for the distributi…
Beyond Expansion III: Reciprocal Geodesics
Jean Bourgain, Alex Kontorovich
We prove the existence of infinitely many low-lying and fundamental closed geodesics on the modular surface which are reciprocal, that is, invariant under time reversal. The method…
A note on the Schrodinger maximal function
Jean Bourgain
It is shown that control of the Schrodinger maximal functions for requires
Sharp bounds for the cubic Parsell-Vinogradov system in two dimensions
Jean Bourgain, Ciprian Demeter, Shaoming Guo
We prove a sharp decoupling for a certain two dimensional surface in R^9. As an application, we obtain the full range of expected estimates for the cubic Parsell-Vinogradov system…
Nonlinear Roth type theorems in finite fields
Jean Bourgain, Mei-Chu Chang
We obtain smoothing estimates for certain nonlinear convolution operators on prime fields, leading to quantitative nonlinear Roth type theorems. Compared with the usual linear sett…