All Outputs (2)

A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem (2023)
Journal Article
Cook, B., Hughes, K., Li, Z. K., Mudgal, A., Robert, O., & Yung, P. (2024). A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem. Mathematika, 70(1), Article e12231. https://doi.org/10.1112/mtk.12231

We interpret into decoupling language a refinement of a 1973 argument due to Karatsuba on Vinogradov's mean value theorem. The main goal of our argument is to answer what precisely solution counting in older partial progress on Vinogradov's mean valu... Read More about A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem.

Discrete restriction estimates for forms in many variables (2023)
Journal Article
Cook, B., Hughes, K., & Palsson, E. (2023). Discrete restriction estimates for forms in many variables. Proceedings of the Edinburgh Mathematical Society, 66(4), 923–939. https://doi.org/10.1017/s0013091523000366

We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work of Birch. To do so, we use a variant of Bourgain’s arithmetic version of the Tomas–Stein method and Magyar’s decomposition of the Fourier transform of... Read More about Discrete restriction estimates for forms in many variables.