On Waring-Goldbach problem with Piatetski-Shapiro primes

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2018

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Abstract

In this paper, we show that all sufficiently large natural numbers satisfying certain local conditions can be written as the sum of kth powers of Piatetski-Shapiro primes, thereby establishing a variant of Waring-Goldbach problem with primes from a sparse sequence.

Source Title

Journal of Number Theory

Publisher

Academic Press

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Keywords

Circle method, Exponential sums, Piatetski-Shapiro, Van der Corput, Waring-Goldbach, Weyl sums

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http://hdl.handle.net/11693/49913

Published Version (Please cite this version)

https://doi.org/10.1016/j.jnt.2017.09.018

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Scholarly Publications - Mathematics

Language

English

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Article