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On the ergodic Waring-Goldbach problem. (English) Zbl 1489.37008

Summary: 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.

MSC:

37A30 Ergodic theorems, spectral theory, Markov operators
37A44 Relations between ergodic theory and number theory
37A46 Relations between ergodic theory and harmonic analysis
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