On the Waring-Goldbach Problem for One Square and Five Cubes in Short Intervals

被引：0
作者：
Fei Xue
Min Zhang
Jinjiang Li
机构：
[1] China University of Mining and Technology,Department of Mathematics
[2] Beijing Information Science and Technology University,School of Applied Science
来源：
Czechoslovak Mathematical Journal | 2021年 / 71卷
关键词：
Waring-Goldbach problem; Hardy-Littlewood method; exponential sum; short interval; 11P05; 11P32; 11P55;
D O I：
暂无
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学科分类号：
摘要：
Let N be a sufficiently large integer. We prove that almost all sufficiently large even integers n ∈ [N − 6U, N + 6U] can be represented as {n=p12+p23+p33+p43+p53+p63|p12−N6|≤U,|pi3−N6|≤U,i=2,3,4,5,6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ {\matrix{ {n = p_1^2 + p_2^3 + p_3^3 + p_4^3 + p_5^3 + p_6^3} \hfill \cr {\left| {p_1^2 - {N \over 6}} \right| \le U,\,\,\,\left| {p_i^3 - {N \over 6}} \right| \le U,\,\,\,i = 2,3,4,5,6} \hfill \cr } } \right.$$\end{document} where U = N1−δ+ε with δ ⩽ 8/225.
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页码：563 / 589
页数：26
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