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Learn about cyclotomic fields in this graduate-level mathematics lecture from the 2025 Summer School at IMPA. Explore advanced topics in algebraic number theory including algebraic integers, rings of algebraic integers of number fields, bases and discriminants, ideals and prime ideals, class groups, unique factorization, ideal norms, discriminants and ramification, fundamental equality, quadratic fields, quadratic reciprocity law, cyclotomic fields, Dirichlet's unit theorem, and zeta functions and L-series of number fields with the class number formula. Drawing from classical texts by Borevich, Shafarevich, Endler, Ribenboim and Samuel, gain deep insights into this fundamental area of pure mathematics through detailed theoretical discussions and proofs presented by Professor Hossein Movasati.
