Discorrelation Between Primes in Short Intervals and Polynomial Phases

Kaisa Matomäki; Xuancheng Shao

doi:10.1093/imrn/rnz188

Discorrelation Between Primes in Short Intervals and Polynomial Phases

Kaisa Matomäki, Xuancheng Shao

Mathematics

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Abstract

Let H = Nθ, θ > 2/3 and k ≥ 1. We obtain estimates for the following exponential sum over primes in short intervals: 'Equation Presented' where g is a polynomial of degree k. As a consequence of this in the special case g(n) = αnk, we deduce a short interval version of the Waring-Goldbach problem.

Original language	English
Pages (from-to)	12330-12355
Number of pages	26
Journal	International Mathematics Research Notices
Volume	2021
Issue number	16
DOIs	https://doi.org/10.1093/imrn/rnz188
State	Published - Aug 1 2021

Bibliographical note

Funding Information:
This work was supported by the Academy of Finland [285894 to K.M.] and National Science Foundation [DMS-1802224 to X.S.].

Publisher Copyright:
© 2019 The Author(s).

ASJC Scopus subject areas

Mathematics (all)

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10.1093/imrn/rnz188

Cite this

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abstract = "Let H = Nθ, θ > 2/3 and k ≥ 1. We obtain estimates for the following exponential sum over primes in short intervals: 'Equation Presented' where g is a polynomial of degree k. As a consequence of this in the special case g(n) = αnk, we deduce a short interval version of the Waring-Goldbach problem.",

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N2 - Let H = Nθ, θ > 2/3 and k ≥ 1. We obtain estimates for the following exponential sum over primes in short intervals: 'Equation Presented' where g is a polynomial of degree k. As a consequence of this in the special case g(n) = αnk, we deduce a short interval version of the Waring-Goldbach problem.

AB - Let H = Nθ, θ > 2/3 and k ≥ 1. We obtain estimates for the following exponential sum over primes in short intervals: 'Equation Presented' where g is a polynomial of degree k. As a consequence of this in the special case g(n) = αnk, we deduce a short interval version of the Waring-Goldbach problem.

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Discorrelation Between Primes in Short Intervals and Polynomial Phases

Abstract

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