Discrete restriction estimates for forms in many variables

Cook, Brian; Hughes, Kevin; Palsson, Eyvindur

Abstract

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 the indicator function of the integer points on a hypersurface.

• Journal Article Type: Article
• Online Publication Date: Sep 18, 2023
• Publication Date: 2023-11
• Deposit Date: Oct 17, 2023
• Publicly Available Date: Oct 17, 2023
• Print ISSN: 0013-0915
• Electronic ISSN: 1464-3839
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 66
• Issue: 4
• Pages: 923–939
• DOI: https://doi.org/10.1017/s0013091523000366
• Keywords: discrete restriction estimates, the circle method, Diophantine equations in many variables
• Public URL: http://researchrepository.napier.ac.uk/Output/3197993