The exceptional set for sums of unlike powers of primes

Zhao, Li

doi:10.1007/s10114-014-3661-y

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Cited by 7 publications

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“…and he obtained the exceptional set is O(N(log N) − (30/47)+ϵ ). Tis result has been improved by Bauer [2], Bauer [3], and Zhao [4], and the latest result is O(N 1− (1/16)+ϵ ). For general k ⩾ 5, the best result was given by Hofman and Yu [5] which is O(N 1− (47/420•2 s )+ϵ ) where s � [k + 1/2].…”

Section: Introductionmentioning

confidence: 99%

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Sums of One Prime Power and Four Prime Cubes in Short Intervals

Huang

Pan

et al. 2023

Journal of Mathematics

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Let k ⩾ 1 be an integer. In this study, we derive an asymptotic formula for the average number of representations of integers n = p 1 k + p 2 3 + p 3 3 + p 4 3 + p 5 3 in short intervals, where p 1 , p 2 , p 3 , p 4 , p 5 are prime numbers.

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Section: Introductionmentioning

confidence: 99%

“…with k ⩾ 4. Let E(k, N) be the number of positive even integers n up to N which cannot be written in the form (4). Tey established that E(k, N) ≪ N 1− θ(k)+ϵ , here…”

Section: Introductionmentioning

confidence: 99%