Papers

  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.

Talks

  • 21 July 2025: On the distribution of zeros of $\zeta(s)$ (Slides) (Recording)

  • 9 Dec 2024 (with Ruiyang Tang and Siyu Liu): Inverse Galois problem (Slides)

  • 16 Oct 2024: Special values of the Riemann zeta function (Slides) (Recording EP1 EP2)

  • 28 Feb 2024 (with May Jiang, Qing Su, and Hantang Guo): Introduction to $p$-adic Analysis (Slides) (Recording)

  • 11 Oct 2023: Ray Reflection and Rational Approximation (Notes) (Recording)

  • 6 June 2023 (with Yi Liu, Daya Singh, and Tairan Wang): Axiom of Choice: Equivalents, Consequences, and Independence (Slides)

  • 10 Mar 2023: Ellipses, Pendulum, and Double Periodicity (Notes) (Recording)

  • 28 Oct 2022: Bounded gaps between primes (Slides) (Recording)

The recordings are also available on Bilibili.