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arXiv · 2605.24109

Decoupling for AD-regular sets on the parabola

Ciprian Demeter·Yuqiu Fu
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Abstract

We improve the decoupling exponent for functions with spectrum inside AD-regular collections of arcs on the parabola. We achieve this by incorporating recent Szemer\'{e}di--Trotter-type estimates into the bootstrapping argument from \cite{BD}. As an application, our results complement, and in some cases improve earlier results \cite{chang2022decoupling} for arithmetic Cantor sets.

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Ciprian Demeter, Yuqiu Fu. 2026-05-22. Decoupling for AD-regular sets on the parabola. https://arxiv.org/abs/2605.24109

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