混合素数幂的 Diophantine 不等式的例外集
数论
2026-04-27 v1
摘要
设 λ 1 , λ 2 , λ 3 , λ 4 , λ 5 , λ 6 , λ 7 \lambda_1, \lambda_2, \lambda_3,\lambda_4,\lambda_5,\lambda_6,\lambda_7 λ 1 , λ 2 , λ 3 , λ 4 , λ 5 , λ 6 , λ 7 λ 1 / λ 2 \lambda_1/\lambda_2 λ 1 / λ 2 V \mathcal{V} V δ > 0 \delta >0 δ > 0 k ≥ 5 k\geq 5 k ≥ 5 ε > 0 \varepsilon >0 ε > 0 ∣ λ 1 p 1 2 + λ 2 p 2 3 + λ 3 p 3 3 + λ 4 p 4 3 + λ 5 p 5 3 + λ 6 p 6 4 + λ 7 p 7 k − υ ∣ < υ − δ \left | \lambda_1p_1^2 + \lambda_2p_2^3 + \lambda_3p_3^3 + \lambda_4p_4^3 + \lambda_5p_5^3 + \lambda_6p_6^4 + \lambda_7p_7^k - \upsilon \right | <{\upsilon}^{-\delta} λ 1 p 1 2 + λ 2 p 2 3 + λ 3 p 3 3 + λ 4 p 4 3 + λ 5 p 5 3 + λ 6 p 6 4 + λ 7 p 7 k − υ < υ − δ p 1 , p 2 , p 3 , p 4 , p 5 , p 6 , p 7 p_1, p_2, p_3, p_4, p_5, p_6, p_7 p 1 , p 2 , p 3 , p 4 , p 5 , p 6 , p 7 υ ∈ V \upsilon \in \mathcal{V} υ ∈ V υ ≤ X \upsilon \leq X υ ≤ X
引用
@article{arxiv.2604.22147,
title = {The exceptional set for Diophantine inequality with mixed powers of primes},
author = {Yu Fu and Linzhu Fu and Liqun Hu},
journal= {arXiv preprint arXiv:2604.22147},
year = {2026}
}