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Explore algebraic number theory in this graduate-level mathematics lecture from IMPA's 2025 Summer School, focusing on algebraic integers, rings of algebraic integers in number fields, bases, and discriminants. Learn about ideals, prime ideals, class groups, unique factorization, ideal norms, discriminants, differents, and ramification. Delve into fundamental equality, quadratic fields, quadratic reciprocity law, cyclotomic fields, Dirichlet's unit theorem, and zeta functions and L-series of number fields, including the analytic class number formula. Based on foundational texts by Borevich & Shafarevich, Endler, Ribenboim, and Samuel, advance your understanding of advanced number theory concepts under the guidance of Professor Hossein Movasati.
