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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.
Author(s): Andrew Sutherland
NA Pages 
Algebraic Number Theory by Dietrich Burde
This note explains the following topics: Integral ring extensions, Ideals of Dedekind rings, Finiteness of the class number, Dirichlets unit theorem, Splitting and ramification, Cyclotomic fields, Valuations and local fields, The theorem of Kronecker weber.
Author(s): Dietrich Burde
101 Pages
Number Theory by Lars Ake Lindahl
This PDF covers the following topics related to Number Theory : Divisibility, Prime Numbers, The Linear Diophantine Equation , Congruences, Linear Congruences, The Chinese Remainder Theorem, Public-Key Cryptography, Pseudoprimes, Polynomial Congruences with Prime Moduli, Polynomial Congruences with Prime Power Moduli, The Congruence, General Quadratic Congruences, The Legendre Symbol and Gauss’ Lemma, Quadratic Reciprocity, Primitive Roots, Arithmetic Functions, Sums of Squares, Pythagorean Triples, Fermat’s Last Theorem, Continued Fractions, Simple Continued Fractions, Rational Approximations to Irrational Numbers, Periodic Continued Fractions, Continued Fraction Expansion, Pell’s Equation.
Author(s): Lars Ake Lindahl
95 Pages
Number Theory Lecture Notes by Vahagn Aslanyan
This note explains the following topics: Divisibility, Multiplicative functions, Modular arithmetic, Primitive roots, Quadratic residues, Diophantine equations, Quadratic number fields, Chebyshev’s theorem.
Author(s): Vahagn Aslanyan
69 Pages
Theory of Numbers Lecture Notes
This lecture note is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.
Author(s): Prof. Abhinav Kumar
NA Pages