國立清華大學 數學系

Abstract:

Modular forms are complex-valued functions with many symmetries defined on the complex upper half-plane. Their Fourier coefficients often carry rich arithmetic or combinatorial meanings. As a result, many important problems in number theory can be solved by studying modular forms. (Among them, the Fermat Last Theorem is perhaps the most well-known.) In this talk, we will review several beautiful applications of modular forms in number theory from the early days of modular forms. The talk will be accessible to undergraduate students.