Sign-patterns of Certain Infinite Products
Undergraduate project, Sun Yat-sen University, 2025
Z. Huang, T. Huber, J. McLaughlin, P. Wang, D. Ye and Y. Xu, Sign-patterns of Certain Infinite Products, Annals of Combinatorics (2026).
Teaching and Projects
Functions of One Complex Variable
Undergraduate course, Sun Yat-sen University, 2025
This course is designed to introduce basic notion of complex analysis covering the complex number field and its geometry, the point of infinity and the Riemann sphere, analytic (holomorphic) and meromorphic functions, the Cauchy Theorem, the Cauchy’s formula, the Identity Principle, the Open Mapping Theorem, the Maximum Modulus Principle, the Argument Principle and the Rouche Theorem and their applications to the zero-counting of some analytic function, conformal mappings, analytic continuations, and etc. if time permits.
Computing the determinant of the operator \(U_{p}\)
Graduate project, Sun Yat-sen University, 2025
X. Huang, T. Huber and D. Ye, On the determinant of \(U_{p}\) on \(M_{k}(p,\chi)\) Ramanujan J. 67 (2025), no. 2, 39.
Advanced Number Theory
Graduate course, Sun Yat-sen University, 2024
Topic: Algebraic number theory from the global perspective covering number fields and their rings of integers and their discriminants and ideals and their norms and traces, the finiteness of an ideal class group and its applications to Diophantine equations, the Dirichlet Unit Theorem, the Dedekind Theorem for ramified primes over \(\mathbb{Q}\), the prime factorizations over a Galois extension and the Artin reciprocity law over \(\mathbb{Q}\) and its implication to the quadratic reciprocity law.
Advanced Number Theory
Graduate course, Sun Yat-sen University, 2023
Topic: Algebraic number theory from the global perspective covering number fields and their rings of integers and their discriminants and ideals and their norms and traces, the quadratic reciprocity law, the finiteness of an ideal class group and its applications to Diophantine equations, the Dirichlet Unit Theorem and the fundamental units of real quadratic fields and their construction via continued fractions.
On the vanishing of the Fourier coefficients of CM eta quotients
Graduate project, Sun Yat-sen University, 2023
T. Huber, C. Liu, J. McLaughlin, D. Ye, M. Yuan and S. Zhang, On the vanishing of the coefficients of CM eta quotients, Proceedings of the Edinburgh Mathematical Society, 66 (2023), 1202-1216.
Representations of squares by septenary quadratic forms and Shimura lifts
Graduate project, Sun Yat-sen University, 2023
H. Chen, D. Ye and M. Yuan, On a remark of Cooper, Lam and Ye, Colloquium Mathematicum, 171 (2023), no.1, 127–144.
Advanced Number Theory
Graduate course, Sun Yat-sen University, 2022
Topic: Modular forms and Riemann surfaces.
On conjectures of Z.-H. Sun
Undergraduate project, Sun Yat-sen University, 2022
Y. Ding, D. Gu, T. Huang, Q. Jiang and D. Ye, On conjectures of Z.-H. Sun, Results in Mathematics, 77 (2022), no.3, Paper No. 105.
Advanced Number Theory
Graduate course, Sun Yat-sen University, 2021
Topic: Modular forms.
Powers of certain theta products
Undergraduate project, Sun Yat-sen University, 2019
Z. Cheng, J. Wang and D. Ye, Powers of certain theta products, Mathematical Reports, 25 (2023), 577-587.