Mark Lewko

collaborators

5 papers

math.CA2026

A bilinear approach to the finite field restriction problem, II

Mark Lewko

Let $P_{3}$ denote the three-dimensional paraboloid over a finite field of prime order in which $- 1$ is not a square. We prove that the Fourier extension operator associated with $P_…

math.CA2026

The Sidon Decomposition Problem in Abelian Groups of Bounded Torsion

Mark Lewko

Let $G$ be a compact abelian group whose dual group $I^ = G$ has bounded torsion. In 1967, Malliavin-Brameret and Malliavin proved that every Sidon set in $I^$ is a finite…

math.CO2026

A Fourier-Free Density-Increment Proof of Roth's Theorem

Mark Lewko

We give an elementary, Fourier-free proof of Roth's theorem. The proof follows Roth's original density-increment strategy, but replaces the usual Fourier-analytic step with a direc…

math.CA2026

A bilinear approach to the finite field restriction problem

Mark Lewko

Let $P$ denote the $3$ -dimensional paraboloid over a finite field of odd characteristic in which $- 1$ is not a square. We show that the Fourier extension operator associated with $…

math.NT2026

An improved non-linear Roth-type theorem in finite fields

Mark Lewko

Let $F$ be a finite field of odd characteristic. We prove that any set $A \subset F$ with $∣ A ∣ \geq C ∣ F ∣^{5/6}$ contains a nontrivial quadratic progression $(x, x+y, x+y^2), y\neq 0.…