On the ergodic Waring–Goldbach problem

Anderson, Theresa C.; Cook, Brian; Hughes, Kevin; Kumchev, Angel

Abstract

We prove an asymptotic formula for the Fourier transform of the arithmetic surface measure associated to the Waring–Goldbach problem and provide several applications, including bounds for discrete spherical maximal functions along the primes and distribution results such as ergodic theorems.

Citation

Anderson, T. C., Cook, B., Hughes, K., & Kumchev, A. (2022). On the ergodic Waring–Goldbach problem. Journal of Functional Analysis, 282(5), Article 109334. https://doi.org/10.1016/j.jfa.2021.109334

• Journal Article Type: Article
• Acceptance Date: Oct 29, 2021
• Online Publication Date: Dec 1, 2021
• Publication Date: 2022-03
• Deposit Date: Nov 21, 2022
• Journal: Journal of Functional Analysis
• Print ISSN: 0022-1236
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 282
• Issue: 5
• Article Number: 109334
• DOI: https://doi.org/10.1016/j.jfa.2021.109334
• Keywords: Circle method, Fourier analysis, Waring–Goldbach problem, Discrete maximal function
• Public URL: http://researchrepository.napier.ac.uk/Output/2963275