# 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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topZhao 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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