On the Waring–Goldbach problem with small non-integer exponent

M. Z. Garaev

doi:10.4064/aa108-3-8

On the Waring–Goldbach problem with small non-integer exponent

Acta Arithmetica ◽

10.4064/aa108-3-8 ◽

2003 ◽

Vol 108 (3) ◽

pp. 297-302 ◽

Cited By ~ 9

Author(s):

M. Z. Garaev

Keyword(s):

Goldbach Problem ◽

Integer Exponent

Download Full-text

On the Waring–Goldbach problem for squares, cubes and higher powers

The Ramanujan Journal ◽

10.1007/s11139-020-00334-2 ◽

2021 ◽

Author(s):

Min Zhang ◽

Jinjiang Li

Keyword(s):

Goldbach Problem

Download Full-text

Enlarged major arcs in the Waring–Goldbach problem

International Journal of Number Theory ◽

10.1142/s1793042116500123 ◽

2016 ◽

Vol 12 (01) ◽

pp. 205-217 ◽

Cited By ~ 6

Author(s):

Taiyu Li

Keyword(s):

Short Note ◽

Circle Method ◽

Goldbach Problem

In this short note, we treat the enlarged major arcs of circle method in the Waring–Goldbach problem.

Download Full-text

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

Open Mathematics ◽

10.1515/math-2017-0130 ◽

2017 ◽

Vol 15 (1) ◽

pp. 1517-1529

Author(s):

Zhao Feng

Keyword(s):

Short Intervals ◽

Exceptional Sets ◽

Goldbach Problem ◽

Almost All

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., $\begin{array}{} N=p_1^3+ \ldots +p_j^3 \end{array} $ with $\begin{array}{} |p_i-(N/j)^{1/3}|\leq N^{1/3- \delta +\varepsilon} (1\leq i\leq j), \end{array} $ for some $\begin{array}{} 0 \lt \delta\leq\frac{1}{90}. \end{array} $ Furthermore, we give the quantitative relations between the length of short intervals and the size of exceptional sets.

Download Full-text