36 citations · 95 across the 23 of their papers we have counts for
5 papers · 1 filter
On the Hardy-Littlewood maximal function for the cube
Jean Bourgain
It is shown that the Hardy-Littlewood maximal function associated to the cube in obeys dimensional free bounds in fir . Earlier work only covered the range…
Monotone Boolean functions capture their primes
Jean Bourgain
It is shown that monotone Boolean functions on the Boolean cube capture the expected number of primes, under he usual identification by binary expansion. This answers a question po…
A prime number theorem for the majority function
Jean Bourgain
In the paper, the occurrence of zeros and ones in the binary expansion of the primes is studied. In particular the statement in the title is established. The proof is unconditional…
A modular Szemeredi-Trotter theorem for hyperbolas
Jean Bourgain
We establish a Szemeredi-Trotter type result for hyperbolas in
Partial quotients and representation of rational numbers
Jean Bourgain
It is shown that there is an absolute constant such that any rational , admits a representation as a finite sum w…