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On the ergodic Waring–Goldbach problem

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


Theresa C. Anderson

Brian Cook

Kevin Hughes

Angel Kumchev


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.


Anderson, T. C., Cook, B., Hughes, K., & Kumchev, A. (2022). On the ergodic Waring–Goldbach problem. Journal of Functional Analysis, 282(5), Article 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
Keywords Circle method, Fourier analysis, Waring–Goldbach problem, Discrete maximal function
Public URL