Introduction to Analytic Number Theory - Komaravolu Chandrasekharan

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Sommaire:
I The unique factorization theorem.- ? 1. Primes.- ? 2. The unique factorization theorem.- ? 3. A second proof of Theorem 2.- ?4. Greatest common divisor and least common multiple.- ? 5. Farey sequences.- ? 6. The infinitude of primes.- II Congruences.- ? 1. Residue classes.- ? 2. Theorems of Euler and of Fermat.- ? 3. The number of solutions of a congruence.- III Rational approximation of irrationals and Hurwitz's theorem.- ? 1. Approximation of irrationals.- ? 2. Sums of two squares.- ? 3. Primes of the form 4k?.- ?4. Hurwitz's theorem.- IV Quadratic residues and the representation of a number as a sum of four squares.- ? 1. The Legendre symbol.- ? 2. Wilson's theorem and Euler's criterion.- ? 3. Sums of two squares.- ? 4. Sums of four squares.- V The law of quadratic reciprocity.- ? 1. Quadratic reciprocity.- ? 2. Reciprocity for generalized Gaussian sums.- ? 3. Proof of quadratic reciprocity.- ? 4. Some applications.- VI Arithmetical functions and lattice points.- ? 1. Generalities.- ? 2. The lattice point function r(n).- ? 3. The divisor function d(n).- ? 4. The functions ?(n).- ? 5. The M?bius functions ?(n).- ? 6. Euler's function ?(n).- VII Chebyshev's therorem on the distribution of prime numbers.- ? 1. The Chebyshev functions.- ? 2. Chebyshev's theorem.- ? 3. Bertrand's postulate.- ? 4. Euler's identity.- ? 5. Some formulae of Mertens.- VIII Weyl's theorems on uniforms distribution and Kronecker's theorem.- ? 1. Introduction.- ? 2. Uniform distribution in the unit interval.- ? 3. Uniform distribution modulo 1.- ? 4. Weyl's theorems.- ? 5. Kronecker's theorem.- IX Minkowski's theorem on lattice points in convex sets.- ? 1. Convex sets.- ? 2. Minkowski's theorem.- ? 3. Applications.- XDirichlet's theorem on primes in an arithmetical progression.- ? 1. Introduction.- ? 2. Characters.- ? 3. Sums of characters, orthogonality relations.- ? 4. Dirichlet series, Landau's theorem.- ? 5. Dirichlet's theorem.- XI The prime number theorem.- ? 1. The non-vanishing of ? (1 + it).- ? 2. The Wiener-Ikehara theorem.- ? 3. The prime number theorem.- A list of books.- Notes.