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Number Theory Lecture Notes by Andrew Sutherland

Number Theory Lecture Notes by Andrew Sutherland

Number Theory Lecture Notes by Andrew Sutherland

This note in number theory explains standard topics in algebraic and analytic number theory. Topics covered includes: Absolute values and discrete valuations, Localization and Dedekind domains, ideal class groups, factorization of ideals, Etale algebras, norm and trace, Ideal norms and the Dedekind-Kummer thoerem, Galois extensions, Frobenius elements, Complete fields and valuation rings, Local fields and Hensel's lemmas , Extensions of complete DVRs, Totally ramified extensions and Krasner's lemma , Dirichlet's unit theorem, Riemann's zeta function and the prime number theorem, The functional equation , Dirichlet L-functions and primes in arithmetic progressions, The analytic class number formula, The Kronecker-Weber theorem, Class field theory, The main theorems of global class field theory, Tate cohomology, profinite groups, infinite Galois theory, Local class field theory, Global class field theory and the Chebotarev density theorem.

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Number Theory Lecture Notes by Andrew Sutherland

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This note in number theory explains standard topics in algebraic and analytic number theory. Topics covered includes: Absolute values and discrete valuations, Localization and Dedekind domains, ideal class groups, factorization of ideals, Etale algebras, norm and trace, Ideal norms and the Dedekind-Kummer thoerem, Galois extensions, Frobenius elements, Complete fields and valuation rings, Local fields and Hensel's lemmas , Extensions of complete DVRs, Totally ramified extensions and Krasner's lemma , Dirichlet's unit theorem, Riemann's zeta function and the prime number theorem, The functional equation , Dirichlet L-functions and primes in arithmetic progressions, The analytic class number formula, The Kronecker-Weber theorem, Class field theory, The main theorems of global class field theory, Tate cohomology, profinite groups, infinite Galois theory, Local class field theory, Global class field theory and the Chebotarev density theorem.

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