# Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem

Open Mathematics (2017)

• Volume: 15, Issue: 1, page 1517-1529
• ISSN: 2391-5455

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## Abstract

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In this paper, we are able to prove that almost all integers n satisfying some necessary congruence conditions are the sum of j almost equal prime cubes with j = 7, 8, i.e., [...] N=p13+…+pj3 $\begin{array}{c}N={p}_{1}^{3}+...+{p}_{j}^{3}\end{array}$ with [...] |pi−(N/j)1/3|≤N1/3−δ+ε(1≤i≤j), $\begin{array}{c}|{p}_{i}-{\left(N/j\right)}^{1/3}|\le {N}^{1/3-\delta +\epsilon }\left(1\le i\le j\right),\end{array}$ for some [...] 0<δ≤190. $\begin{array}{c}0\delta \le \frac{1}{90}.\end{array}$ Furthermore, we give the quantitative relations between the length of short intervals and the size of exceptional sets.

## How to cite

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Zhao Feng. "Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem." Open Mathematics 15.1 (2017): 1517-1529. <http://eudml.org/doc/288293>.

@article{ZhaoFeng2017,
abstract = {In this paper, we are able to prove that almost all integers n satisfying some necessary congruence conditions are the sum of j almost equal prime cubes with j = 7, 8, i.e., [...] N=p13+…+pj3 $\begin\{array\}\{\} N=p_1^3+ \ldots +p_j^3 \end\{array\}$ with [...] |pi−(N/j)1/3|≤N1/3−δ+ε(1≤i≤j), $\begin\{array\}\{\} |p_i-(N/j)^\{1/3\}|\le N^\{1/3- \delta +\varepsilon \} (1\le i\le j), \end\{array\}$ for some [...] 0<δ≤190. $\begin\{array\}\{\} 0 \delta \le \frac\{1\}\{90\}. \end\{array\}$ Furthermore, we give the quantitative relations between the length of short intervals and the size of exceptional sets.},
author = {Zhao Feng},
journal = {Open Mathematics},
keywords = {Circle method; Exponential sums over primes; Short intervals; Quantitative relations},
language = {eng},
number = {1},
pages = {1517-1529},
title = {Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem},
url = {http://eudml.org/doc/288293},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Zhao Feng
TI - Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 1517
EP - 1529
AB - In this paper, we are able to prove that almost all integers n satisfying some necessary congruence conditions are the sum of j almost equal prime cubes with j = 7, 8, i.e., [...] N=p13+…+pj3 $\begin{array}{} N=p_1^3+ \ldots +p_j^3 \end{array}$ with [...] |pi−(N/j)1/3|≤N1/3−δ+ε(1≤i≤j), $\begin{array}{} |p_i-(N/j)^{1/3}|\le N^{1/3- \delta +\varepsilon } (1\le i\le j), \end{array}$ for some [...] 0<δ≤190. $\begin{array}{} 0 \delta \le \frac{1}{90}. \end{array}$ Furthermore, we give the quantitative relations between the length of short intervals and the size of exceptional sets.
LA - eng
KW - Circle method; Exponential sums over primes; Short intervals; Quantitative relations
UR - http://eudml.org/doc/288293
ER -

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