Steve Fan

Steve Fan

he/his

Publications & Preprints

  1. A family of analogues to the Robin criterion (with Mits Kobayashi and Grant Molnar), preprint 2025. arXiv:2511.02106
  2. Sárközy's theorem in \(\mathbb{F}_q[t]\) via the van der Corput property (with Andrew Lott), preprint 2025. arXiv:2510.27581
  3. The maximal order of the shifted-prime divisor function (with Paul Pollack), preprint 2025. arXiv:2510.14167
  4. The Hardy–Ramanujan inequality for sifted sets and its applications, preprint 2025. arXiv:2508.06005
  5. Counting primes with a given primitive root, uniformly (with Paul Pollack), preprint, 2025. arXiv:2505.05601. To appear in Mathematika.
  6. Extremal elasticity of quadratic orders (with Paul Pollack), The ideal theory and arithmetic of rings, monoids, and semigroups (Palermo, 2024). Edited by S. T. Chapman. AMS Contemporary Mathematics series, to appear.
  7. The typical elasticity of a quadratic order (with Paul Pollack), preprint 2024. arXiv:2411.09063
  8. The shifted prime-divisor function over shifted primes, Ramanujan J. 66 (2025), no. 44, 1–46.
  9. Shifted prime-divisors (with Carl Pomerance), preprint, 2024. arXiv:2401.10427. To appear in a Springer volume dedicated to Helmut Maier on his 70th birthday and edited by J. Friedlander, C. Pomerance, and M. Rassias.
  10. Weighted Erdős–Kac theorems via computing moments, Acta Arith. 217 (2025), no. 2, 99–158.
  11. On a super telescoping sum representing binomial coefficients, to appear in Rocky Mountain J. Math., 2023.
  12. Numerically explicit estimates for the distribution of rough numbers, J. Number Theory 260 (2024), 120–150.
  13. An inequality related to the sieve of Eratosthenes (with Carl Pomerance), J. Number Theory 254 (2024), 169–183.
  14. An inequality for the distribution of numbers free of small prime factors, Integers 22 (2022), #A26, 12 pp.
  15. The second largest Balaban index (sum-Balaban index) of unicyclic graphs (with Wei Fang, Yubin Gao and Zhongshan Li), J. Math. Res. Appl. 37 (2017), 391–403.
  16. A finite difference scheme for semilinear space-fractional diffusion equations with time delay (with Wanrong Cao, Zhaopeng Hao and Zhizhong Sun), Appl. Math. Comput. 275 (2016), 238–254.