Exponential sums over primes in short intervals

Bingrong Huang; Zhiwei Wang

doi:10.1016/j.jnt.2014.09.004

Exponential sums over primes in short intervals

Bingrong Huang^*, Zhiwei Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Let A(n) be the von Mangoldt function, x real and 2 ≤ y ≤ x. This paper improves the estimate on the exponential sum over primes in short intervals. Sk(x,y;α)=∑x<n≤x+y A(n)e(n^kα) when k≥ 4 for all α ∈ [0, 1]. And then combined with the Hardy-Littlewood method, this enables us to give some short interval variants of Hua's theorems in additive prime number theory.

Original language	English
Pages (from-to)	204-219
Number of pages	16
Journal	Journal of Number Theory
Volume	148
DOIs	https://doi.org/10.1016/j.jnt.2014.09.004
State	Published - 1 Mar 2015
Externally published	Yes

Keywords

Exponential sums
Short intervals
Von Mangoldt function

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10.1016/j.jnt.2014.09.004

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abstract = "Let A(n) be the von Mangoldt function, x real and 2 ≤ y ≤ x. This paper improves the estimate on the exponential sum over primes in short intervals. Sk(x,y;α)=∑xkα) when k≥ 4 for all α ∈ [0, 1]. And then combined with the Hardy-Littlewood method, this enables us to give some short interval variants of Hua's theorems in additive prime number theory.",

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AB - Let A(n) be the von Mangoldt function, x real and 2 ≤ y ≤ x. This paper improves the estimate on the exponential sum over primes in short intervals. Sk(x,y;α)=∑xkα) when k≥ 4 for all α ∈ [0, 1]. And then combined with the Hardy-Littlewood method, this enables us to give some short interval variants of Hua's theorems in additive prime number theory.

KW - Exponential sums

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Exponential sums over primes in short intervals

Abstract

Keywords

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