Results 1 to 10 of about 126,211 (116)
Waring–Goldbach Problem of Even Powers in Short Intervals
Journal of Mathematics, 2021 In this paper, we study the average behaviour of the representations of n=p12+p24+p34+p4k over short intervals for k≥4, where p1,p2,p3,p4 are prime numbers. This improves the previous results.
Liqun Hu, Tanhui Zhang
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Exceptional set in Waring–Goldbach problem for sums of one square and five cubes
AIMS Mathematics, 2022 Let $ N $ be a sufficiently large integer. In this paper, it is proved that, with at most $ O\big(N^{4/9+\varepsilon}\big) $ 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_6^3 $, where $
Jinjiang Li +3 more
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On the Waring--Goldbach problem for eighth and higher powers [PDF]
Journal of the London Mathematical Society, 2015 Recent progress on Vinogradov's mean value theorem has resulted in improved estimates for exponential sums of Weyl type. We apply these new estimates to obtain sharper bounds for the function $H(k)$ in the Waring--Goldbach problem.
Angel V. Kumchev, D. Wooley, Trevor
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A density version of Waring-Goldbach problem
International Journal of Number Theory, 2023 In this paper, we study a density version of the Waring-Goldbach problem. Suppose that A is a subset of the primes, and the lower density of A in the primes is larger than 1/2. Let k be a positive integer other than 1, 2, 4, 8, and 9. We prove that every
Gao, Meng
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On the Waring–Goldbach problem for seventh and higher powers [PDF]
Monatshefte für Mathematik, 2016 We apply recent progress on Vinogradov's mean value theorem to improve bounds for the function $H(k)$ in the Waring-Goldbach problem. We obtain new results for all exponents $k \ge 7$, and in particular establish that for large $k$ one has \[H(k)\le (4k ...
Kumchev, Angel, Wooley, Trevor D
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Waring-Goldbach problem in short intervals [PDF]
Israel Journal of Mathematics, 2019 Let $k\geq2$ and $s$ be positive integers. Let $\theta\in(0,1)$ be a real number. In this paper, we establish that if $s>k(k+1)$ and $\theta>0.55$, then every sufficiently large natural number $n$, subjects to certain congruence conditions, can be ...
Wang, Mengdi
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On the Waring–Goldbach problem for two squares and four cubes
AIMS Mathematics, 2022 Let $ \mathcal{P}_r $ denote an almost–prime with at most $ r $ prime factors, counted according to multiplicity. In this paper, it is proved that for every sufficiently large even integer $ N $, the following equation $ \begin{equation*} N = p_1^2 ...
Min Zhang, Fei Xue, Jinjiang Li
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Improved $\ell^p$-Boundedness for Integral $k$-Spherical Maximal Functions
Discrete Analysis, 2018 Improved $\ell^p$-Boundedness for Integral $k$-Spherical Maximal Functions, Discrete Analysis 2018:10, 18pp. An important role in harmonic analysis is played by the notion of a _maximal function_ (which is actually a non-linear operator on a space of ...
Theresa C. Anderson +3 more
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The exceptional sets of a Waring-Goldbach problem with unequal powers
Xi'an Gongcheng Daxue xuebao, 2021 The representability of positive odd number n=p1+P32+p3k(k∈N and k≥4) was studied. The circle method in additive number theory and the iterative method in the circle method were used to deal with the main arcs and the exponential sum method was used to ...
Doudou ZHU
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On the Waring-Goldbach problem for two squares and four cubes
Open Mathematics, 2023 Let NN be a sufficiently large integer. In this article, it is proved that, with at most O(N112+ε)O\left({N}^{\tfrac{1}{12}+\varepsilon }) exceptions, all even positive integers up to NN can be represented in the form p12+p22+p33+p43+p53+p63{p}_{1}^{2 ...
Zhang Min, Bai Hongxin, Li Jinjiang
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