Mark Lewko

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20112019

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math.CA2019

Counting rectangles and an improved restriction estimate for the paraboloid in $F_{p}^{3}$

Mark Lewko

Given $A \subset F_{p}^{2}$ a sufficiently small set in the plane over a prime residue field, we prove that there are at most $O_{ε} (∣ A ∣^{\frac{99}{41} + ε})$ rectangles with corners in…

math.CA2017

Finite field restriction estimates for the paraboloid in high even dimensions

Alex Iosevich, Doowon Koh, Mark Lewko

We prove that the finite field Fourier extension operator for the paraboloid is bounded from $L^{2} \to L^{r}$ for $r \geq \frac{2 d + 4}{d}$ in even dimensions $d \geq 8$ , which is the optim…

math.CA2012

The Square Variation of Rearranged Fourier Series

Allison Lewko, Mark Lewko

We prove that there exists a rearrangement of the first $N$ elements of the trigonometric system such that the $L^{2}$ -norm of the square variation operator is at most $O_ε(\log^{9/2…

Counting rectangles and an improved restriction estimate for the paraboloid in Fp3​

Finite field restriction estimates for the paraboloid in high even dimensions

The Square Variation of Rearranged Fourier Series

Counting rectangles and an improved restriction estimate for the paraboloid in $F_{p}^{3}$