Automorphic L-function

In number theory and representation theory, an automorphic L-function is a type of complex analytic function that encodes significant arithmetic information about automorphic forms, which are certain types of functions defined on algebraic groups over global fields (like the rational numbers) that exhibit certain symmetries and transformation properties. ### Key Concepts: 1. **Automorphic Forms**: These are generalizations of modular forms, defined on the quotient of a group (often the general linear group) over a number field.