On the ergodic Waring--Goldbach problem

2017/03/08 by Theresa C. Anderson, Anderson, Theresa C., Brian Cook +5
Mathematics · #11 #42 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #math.CA #math.NT #msc:11 #msc:42

paper · pdf · doi:10.48550/arxiv.1703.02713

We elaborated on our introduction and cleaned up some typos

arxiv created 2019/08/07 · arxiv updated 2019/08/09

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.

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