1. Liu, Z. (2025). Explicit quadratic large sieve inequality (arXiv:2505.09637).
  2. Liu, Z. (2023). On sums of Fourier coefficients of cusp forms twisted with additive characters (arXiv:2311.00006).
  3. Liu, Z. (2022). On a weighted sum over multiplicative functions and its applications to the GPY sieve (arXiv:2210.01671).
  4. Liu, Z. (2022). A Corrected Simplified Proof of Chen’s Theorem (arXiv:2203.07871).
  5. Liu, Z. (2022). A Simple Proof of Siegel’s Theorem Using Mellin Transform (arXiv:2202.00635).
  6. Liu, Z. (2022). A Direct Proof of the Prime Number Theorem using Riemann’s Prime-counting Function. Journal of Physics: Conference Series, 2287(1), 012008. (arXiv:2105.05317)
  7. Liu, Z. (2021). PM2.5 Density Prediction Based on a Two-Stage Rolling Forecast Model Using LightGBM. In W. Cao, A. Ozcan, H. Xie, & B. Guan (Eds.), Computing and Data Science (Vol. 1513, pp. 228–248). Springer Nature Singapore.