On the Waring-Goldbach problem for one square and five cubes in short intervals

Fei Xue; Min Zhang; Jinjiang Li

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 2, page 563-589
  • ISSN: 0011-4642

Abstract

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Let N be a sufficiently large integer. We prove that almost all sufficiently large even integers n ∈ [ N - 6 U , N + 6 U ] can be represented as n = p 1 2 + p 2 3 + p 3 3 + p 4 3 + p 5 3 + p 6 3 , p 1 2 - N 6 ≤ U , p i 3 - N 6 ≤ U , i = 2 , 3 , 4 , 5 , 6 , where U = N 1 - δ + ε with δ ≤ 8 / 225 .

How to cite

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Xue, Fei, Zhang, Min, and Li, Jinjiang. "On the Waring-Goldbach problem for one square and five cubes in short intervals." Czechoslovak Mathematical Journal 71.2 (2021): 563-589. <http://eudml.org/doc/298200>.

@article{Xue2021,
abstract = {Let $N$ be a sufficiently large integer. We prove that almost all sufficiently large even integers $n\in [N-6U,N+6U]$ can be represented as \[ n=p\_1^2+p\_2^3+p\_3^3+p\_4^3+p\_5^3+p\_6^3, \Bigl | p\_1^2-\dfrac\{N\}\{6\}\Bigr | \le U, \quad \Bigl | p\_i^3-\dfrac\{N\}\{6\}\Bigr |\le U, \quad i=2,3,4,5,6, \] where $U=N^\{1-\delta +\varepsilon \}$ with $\delta \le 8/225$.},
author = {Xue, Fei, Zhang, Min, Li, Jinjiang},
journal = {Czechoslovak Mathematical Journal},
keywords = {Waring-Goldbach problem; Hardy-Littlewood method; exponential sum; short interval},
language = {eng},
number = {2},
pages = {563-589},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Waring-Goldbach problem for one square and five cubes in short intervals},
url = {http://eudml.org/doc/298200},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Xue, Fei
AU - Zhang, Min
AU - Li, Jinjiang
TI - On the Waring-Goldbach problem for one square and five cubes in short intervals
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 2
SP - 563
EP - 589
AB - Let $N$ be a sufficiently large integer. We prove that almost all sufficiently large even integers $n\in [N-6U,N+6U]$ can be represented as \[ n=p_1^2+p_2^3+p_3^3+p_4^3+p_5^3+p_6^3, \Bigl | p_1^2-\dfrac{N}{6}\Bigr | \le U, \quad \Bigl | p_i^3-\dfrac{N}{6}\Bigr |\le U, \quad i=2,3,4,5,6, \] where $U=N^{1-\delta +\varepsilon }$ with $\delta \le 8/225$.
LA - eng
KW - Waring-Goldbach problem; Hardy-Littlewood method; exponential sum; short interval
UR - http://eudml.org/doc/298200
ER -

References

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