Waring–Goldbach problem for fourth powers with almost equal variables

Yao, Yanjun; Zhang, Meng

doi:10.1007/s10986-016-9337-9

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Cited by 2 publications

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“…Proof. One can refer to the case k = 3 and k = 4 in [17] and [18], respectively. And this is Lemma 2.1 in [16] (in Chinese).…”

Section: Preliminariesmentioning

confidence: 99%

On sums of $k$-th powers with almost equal primes

Zhang¹

2022

Preprint

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For "almost all" sufficiently large N, satisfying necessary congruence conditions and k ≥ 2, we show that there is an asymptotic formula for the number of solutions of the equationThis enlarges the effective range of s for which can be obtained by the method of Mätomaki and Xuancheng Shao [12]. [Discorrelation between primes in short intervals and polynomial phase, Int. Math. Res. Not. IMRN 2021, no. 16, 12330-12355.] The idea is to avoid using the exponential sums (1.2) and Vinogradov mean value theorems in Lemma 2.4 simultaneously. And the main new ingredient is from Kumchev and Liu [9] (see Lemma 2.2).

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“…Proof. One can refer to the case k = 3 and k = 4 in [17] and [18], respectively. And this is Lemma 2.1 in [16] (in Chinese).…”

Section: Preliminariesmentioning

confidence: 99%