Author | Chandrasekharan, K. author |
---|---|
Title | Introduction to Analytic Number Theory [electronic resource] / by K. Chandrasekharan |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1968 |
Connect to | http://dx.doi.org/10.1007/978-3-642-46124-8 |
Descript | VIII, 144 p. online resource |
I The unique factorization theorem -- ยง 1. Primes -- ยง 2. The unique factorization theorem -- ยง 3. A second proof of Theorem 2 -- ยง4. Greatest common divisor and least common multiple -- ยง 5. Farey sequences -- ยง 6. The infinitude of primes -- II Congruences -- ยง 1. Residue classes -- ยง 2. Theorems of Euler and of Fermat -- ยง 3. The number of solutions of a congruence -- III Rational approximation of irrationals and Hurwitzโs theorem -- ยง 1. Approximation of irrationals -- ยง 2. Sums of two squares -- ยง 3. Primes of the form 4kยฑ -- ยง4. Hurwitzโs theorem -- IV Quadratic residues and the representation of a number as a sum of four squares -- ยง 1. The Legendre symbol -- ยง 2. Wilsonโs theorem and Eulerโs criterion -- ยง 3. Sums of two squares -- ยง 4. Sums of four squares -- V The law of quadratic reciprocity -- ยง 1. Quadratic reciprocity -- ยง 2. Reciprocity for generalized Gaussian sums -- ยง 3. Proof of quadratic reciprocity -- ยง 4. Some applications -- VI Arithmetical functions and lattice points -- ยง 1. Generalities -- ยง 2. The lattice point function r(n) -- ยง 3. The divisor function d(n) -- ยง 4. The functions ?(n) -- ยง 5. The Mรถbius functions ?(n) -- ยง 6. Eulerโs function ?(n) -- VII Chebyshevโs therorem on the distribution of prime numbers -- ยง 1. The Chebyshev functions -- ยง 2. Chebyshevโs theorem -- ยง 3. Bertrandโs postulate -- ยง 4. Eulerโs identity -- ยง 5. Some formulae of Mertens -- VIII Weylโs theorems on uniforms distribution and Kroneckerโs theorem -- ยง 1. Introduction -- ยง 2. Uniform distribution in the unit interval -- ยง 3. Uniform distribution modulo 1 -- ยง 4. Weylโs theorems -- ยง 5. Kroneckerโs theorem -- IX Minkowskiโs theorem on lattice points in convex sets -- ยง 1. Convex sets -- ยง 2. Minkowskiโs theorem -- ยง 3. Applications -- X Dirichletโs theorem on primes in an arithmetical progression -- ยง 1. Introduction -- ยง 2. Characters -- ยง 3. Sums of characters, orthogonality relations -- ยง 4. Dirichlet series, Landauโs theorem -- ยง 5. Dirichletโs theorem -- XI The prime number theorem -- ยง 1. The non-vanishing of ? (1 + it) -- ยง 2. The Wiener-Ikehara theorem -- ยง 3. The prime number theorem -- A list of books -- Notes