Results 71 to 80 of about 126,211 (116)

Waring–Goldbach problem involving cubes of primes

Mathematische Zeitschrift, 2020
Using the circle method the authors prove two main results: (a) Every sufficiently large integer is a sum of one prime number, four cubes of primes, and fifteen powers of \(2\). Assuming the Riemann hypothesis the number of powers of two is reduced to seven.
T. Ching, K. Tsang
semanticscholar   +3 more sources

Enlarged major arcs in the Waring–Goldbach problem

International Journal of Number Theory, 2016
In this short note, we treat the enlarged major arcs of circle method in the Waring–Goldbach problem.
Taiyu Li
semanticscholar   +3 more sources

On Waring-Goldbach Problem for Mixed Powers

International Journal of Number Theory, 2017
In this short paper, we investigate exceptional sets in the Waring–Goldbach problem for fifth powers. For example, we show that all but O(N213/214) integers subject to the necessary local conditions can be represented as the sum of 11 fifth powers of primes. This improves the previous result.
Jinjia Li, Min Zhang
semanticscholar   +3 more sources

ON THE WARING–GOLDBACH PROBLEM FOR ONE SQUARE, FOUR CUBES AND ONE BIQUADRATE

Bulletin of the Australian Mathematical Society, 2022
Let N be a sufficiently large integer. We prove that, with at most $O(N^{23/48+\varepsilon })$ exceptions, all even positive integers up to N can be represented in the form $p_1^2+p_2^3+p_3^3+p_4^3+p_5^3+p_6^4$ , where $p_1,p_2,p_3,p_4,p_5,p_6$ are
Jinjia Li, Fei Xue, M. Zhang
semanticscholar   +1 more source

Slim exceptional sets of Waring-Goldbach problem: two squares, two cubes and two biquadrates

Sbornik: Mathematics
Let $N$ be a sufficiently large number. We show that, with at most $O(N^{3/32+\varepsilon})$ exceptions, all even positive integers not exceeding $N$ can be represented in the form $p_1^2+p_2^2+p_3^3+p_4^3+p_5^4+p_6^4$, where $p_1, p_2, …, p_6$ are prime
Shuangrui Tian
semanticscholar   +1 more source

On Waring–Goldbach problem for unlike powers

International Journal of Number Theory, 2018
Let [Formula: see text] denote an almost-prime with at most [Formula: see text] prime factors, counted according to multiplicity. In this paper, it is proved that, for [Formula: see text] and for every sufficiently large even integer [Formula: see text], the equation [Formula: see text] is solvable with [Formula: see text] being an almost-prime ...
Li, Jinjiang, Zhang, Min
openaire   +2 more sources

Exceptional Set in Waring–Goldbach Problem Involving Squares, Cubes and Sixth Powers

, 2021
Let N be a sufficiently large integer. In this paper, it is proved that, with at most O(N 119/270+s) exceptions, all even positive integers up to N can be represented in the form where p1, p2, p3, p4, p5, p6 are prime numbers.
Jinjia Li, M. Zhang, Hao Zhao
semanticscholar   +1 more source

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

The Ramanujan journal, 2020
Let Pr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {P}_r ...
Min Zhang, Jinjia Li
semanticscholar   +1 more source

On a Waring-Goldbach problem involving squares and cubes

Mathematica Slovaca, 2019
Let R(n) denote the number of representations of a natural number n as the sum of two squares and four cubes of primes. In this paper, it is proved that the anticipated asymptotic formula for R(n) fails for at most O(N14+ε) $\begin{array}{}O(N^{\frac{1 ...
Yuhui Liu
semanticscholar   +1 more source

Waring–Goldbach problem: two squares and some unlike powers

Acta Mathematica Hungarica, 2014
This paper shows that every sufficiently large odd integer \(N\) may be written as \[ N=x^2+p_2^2+p_3^3+p_4^4+p_5^5+p_6^6+p_7^7, \] in which the \(p_i\) are prime, and \(x\) is a \(P_6\) almost-prime. Indeed this result is one of a range of theorems in which the final term is replaced by \(p_7^k\) for some \(k\in [6,19]\), and \(x\) is a \(P_r\) almost-
Cai, Yingchun, Mu, Quanwu
openaire   +1 more source