Restriction estimates for toral eigenfunctions and lattice points in spherical regions

Cheng Zhang; Zhifei Zhu

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arXiv · 2606.08650

Restriction estimates for toral eigenfunctions and lattice points in spherical regions

Cheng Zhang·Zhifei Zhu

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Abstract

We establish new $L^2$ restriction estimates for toral eigenfunctions. These estimates are sharp in certain cases, and thus prove a conjecture of Huang-Zhang for smooth submanifolds of large codimension. In particular, they provide new progress toward a conjecture of Bourgain-Rudnick. The proof combines a slicing and packing method with the approximation of the discrete spherical multiplier by Magyar-Stein-Wainger and Magyar.

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Cheng Zhang, Zhifei Zhu. 2026-06-07. Restriction estimates for toral eigenfunctions and lattice points in spherical regions. https://arxiv.org/abs/2606.08650

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