Dongxi Ye

Dongxi Ye

with his kitty Balla (小丸子) on her fourth birthday

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.

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 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.

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.