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A density version for the sum of nine cubes of primes
Abstract
Let ℙ be the set of primes. Suppose that Pi, i=1,2,…,9 are nine subsets of ℙ with relative lower density underlinedℙ(Pi)=μi. When ∑i=19 μi3>8, we prove that every sufficiently large odd integer can be written as n=∑i=19 pi3 with pi ∈ Pi, i=1,2,…,9.
Related
BibTeX
@misc{li2026density,
title = {{A density version for the sum of nine cubes of primes}},
author = {Kaijie Li and Tianze Wang and Xiaodong Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25171},
eprint = {2609.25171},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25171},
}
RIS
TY - UNPB
TI - A density version for the sum of nine cubes of primes
AU - Kaijie Li
AU - Tianze Wang
AU - Xiaodong Zhao
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25171
UR - https://arxiv.org/abs/2609.25171
AB - Let ℙ be the set of primes. Suppose that P_i, i=1,2,…,9 are nine subsets of ℙ with relative lower density underlined_ℙ(P_i)=μ_i. When ∑_i=1^9 μ_i^3>8, we prove that every sufficiently large odd integer can be written as n=∑_i=1^9 p_i^3 with p_i ∈ P_i, i=1,2,…,9.
ER -