國立清華大學 數學系

Abstract In this talk, we introduce L-functions based on explicit examples. An L-function is a Dirichlet series associated to certain mathematical object. We expect that it should satisfies certain nice properties. For example, it should admits meromorphic continuation, has an Euler product, and satisfies certain functional equation. We will give examples of L-functions associated to a Galois representation, an elliptic curve, and a modular form.