Results 61 to 70 of about 496 (82)

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.
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A result on Waring–Goldbach problem for cubes

Lithuanian Mathematical Journal, 2011
Let \(N\) be a large number and \(4 \leq s \leq8\). Let \(E_s(N)\) denote the number of positive integers \(n \leq N\) which cannot be written in the form \[ n = m^3 + p_2^3 +p_3^3 + \cdots + p_s^3, \] with positive integer \(m\) and primes \(p_2, p_3, \ldots , p_s\).
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The Waring–Goldbach problem for cubes with an almost prime

Proceedings of the London Mathematical Society, 2019
This paper shows that every sufficiently large even integer \(N\) can be written in the form \[N=p_1^3+\ldots+p_7^3+x^3\] with \(x\) being the product of two distinct primes. Previously it had been shown by \textit{J. Brüdern} [Ann. Sci. Éc. Norm. Supér. (4) 28, No. 4, 461--476 (1995; Zbl 0839.11045)] that one could handle such representations with \(x\
Kawada, Koichi, Zhao, Lilu
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The Waring–Goldbach problem: one square and five cubes

The Ramanujan Journal, 2013
Suppose that \(p_1, p_2, p_3, p_4, p_5\) are prime numbers and a natural number \(x\) has at most 36 prime factors, counted according to multiplicity. Let \(R(N)\) denote the number of solutions of the following equation \[ N=x^2+p_1^3+p_2^3+p_3^3+p_4^3+p_5^3.
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An improvement on Waring–Goldbach problem for unlike powers

Acta Mathematica Hungarica, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the ergodic Waring–Goldbach problem

Journal of Functional Analysis, 2022
Kevin Hughes, Angel V Kumchev
exaly  

Waring-Goldbach problem for Unlike Powers (II)

2010
研究混合方次的Waring-Goldbach問題,證明除了至多O(N47/48+ε)個例外,所有不超過N的偶數均可表為素數的2,3,4,5次方之和．
Ren, X, Tsang, KM
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On exceptional sets in the Waring–Goldbach problem for fifth powers

Ramanujan Journal, 2022
Gongrui Chen
exaly  

Exceptional sets in Waring-Goldbach problem for fifth powers

Frontiers of Mathematics in China, 2021
exaly  

On a Waring-Goldbach problem involving squares and cubes

Mathematica Slovaca, 2019
Yuhui Liu
exaly