21 papers
Primes of the form
Ben Green, Mehtaab Sawhney
Suppose that is or modulo . We show that there are infinitely many primes of the form with both and prime, and obtain an asymptotic for their nu…
The proportion of permutations fixing a -set
Ben Green, Mehtaab Sawhney
Denote by the limit, as , of the probability that a random permutation on a set of size has an invariant set of size . We give an asymptotic for…
On the maxima of Littlewood polynomials on
Brayden Letwin, Mehtaab Sawhney
A Littlewood polynomial is a polynomial of the form \[ f_n(x)=\sum_{k=0}^n \varepsilon_k x^k \] with . Let be i.i.d. Rademach…
Short proofs in combinatorics, probability and number theory II
Boris Alexeev, Moe Putterman, Mehtaab Sawhney +2
We give a quintet of proofs resulting from questions posed by ErdÅs. These questions concern ordinary lines in planar point sets, sequences with uniformly small exponential sums,…
Short proofs in combinatorics and number theory
Boris Alexeev, Moe Putterman, Mehtaab Sawhney +2
We give a triplet of short proofs, each of which answers a question raised by ErdÅs. The first concerns the small prime factors of , the second concerns whether an a…
On infinite sets with no on a line
Moe Putterman, Mehtaab Sawhney, Gregory Valiant
We give a construction of an infinite set of points in such that any subset has a constant density subset with no three points collinear and…