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Explore algebraic number theory in this graduate-level mathematics lecture from IMPA's 2025 Summer School, where Professor Hossein Movasati delves into algebraic integers, rings of algebraic integers in number fields, bases and discriminants, ideals and prime ideals, class groups and their finiteness, unique factorization, ideal norms, discriminants, different and ramification, fundamental equality, quadratic fields and quadratic reciprocity law, cyclotomic fields, Dirichlet's unit theorem, and zeta functions and L-series of number fields including the analytic class number formula. Learn from key references including works by Borevich and Shafarevich, Endler, Ribenboim, and Samuel while advancing understanding of fundamental concepts in algebraic number theory through this comprehensive mathematical exploration.
