Automorphic Forms

Automorphic forms are mathematical objects that arise in number theory and algebra. They generalize periodic functions and modular forms by extending their properties to more complex spaces, often in relation to symmetries of shapes or algebraic structures. These forms are important in studying the relationships between numbers, especially in areas like modular forms, representation theory, and arithmetic geometry. Essentially, they reveal deep connections between different mathematical realms, enriching our understanding of both number theory and geometry through their intricate structure and the symmetries they embody.