54 citations · 90 across the 6 of their papers we have counts for
10 papers
On restriction estimates for discrete quadratic surfaces
Kevin Henriot, Kevin Hughes
We obtain truncated restriction estimates of an unexpected form for discrete surfaces \begin{align} S = \{\, ( n_1 , \dots , n_d , R( n_1 , \dots, n_d ) ) \,,\, n_i \in [-N,N] \cap…
Discrete restriction estimates of epsilon-removal type for kth-powers and k-paraboloids
Kevin Henriot, Kevin Hughes
We obtain restriction estimates of -removal type for the set of -th powers of integers, and for discrete -dimensional surfaces of the form \[ \{ (n_1,\dots,n_d,n_1^k + \do…
A Discrete Carleson Theorem Along the Primes with a Restricted Supremum
Laura Cladek, Kevin Henriot, Ben Krause +2
Consider the discrete maximal function acting on finitely supported functions on the integers, \[ \mathcal{C}_Λf(n) := \sup_{λ\in Λ} | \sum_{p \in \pm \mathbb{P}} f(n-p) \log |p| \…
On polynomial configurations in fractal sets
Kevin Henriot, Izabella Laba, Malabika Pramanik
We show that subsets of of large enough Hausdorff and Fourier dimension contain polynomial patterns of the form \begin{align*} ( x ,\, x + A_1 y ,\, \dots,\, x + A_{…
Additive equations in dense variables via truncated restriction estimates
Kevin Henriot
We study translation-invariant additive equations of the form in variables , where the are nonz…
Logarithmic bounds for translation-invariant equations in squares
Kevin Henriot
We show that the equation admits non-trivial solutions in any subset of of density , provided that and the coeff…
On systems of complexity one in the primes
Kevin Henriot
Consider a translation-invariant system of linear equations of complexity one, where is an integer matrix. We show that if is a subset of the primes…
Arithmetic progressions in sets of small doubling
Kevin Henriot
We show that if a finite, large enough subset A of an arbitrary abelian group satisfies the small doubling condition |A + A| < (log |A|)^{1 - epsilon} |A|, then A must contain a th…
On arithmetic progressions in A + B + C
Kevin Henriot
Our main result states that when A, B, C are subsets of Z/NZ of respective densities α,β,γ, the sumset A + B + C contains an arithmetic progression of length at least e^{c(\log N)^…
Nair-Tenenbaum bounds uniform with respect to the discriminant
Kevin Henriot
A common problem in analytic number theory is to bound the sum of an arithmetic function over a set of integers. Nair and Tenenbaum found a very general bound that applies to short…