Hida's Theory

Hida’s Theory explores the construction of p-adic automorphic forms, which are special functions exhibiting symmetry under certain mathematical groups, within number theory. It provides a framework for understanding how these forms vary continuously in p-adic families, connecting classical automorphic forms with p-adic analytic properties. Essentially, Hida's work facilitates studying deep relationships between algebraic and analytic structures in number theory, particularly in understanding how certain symmetries and patterns evolve in p-adic contexts, aiding progress in areas like Galois representations and arithmetic geometry.