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Introduction to Analytic Number Theory Softcover reprint of the original 1st ed. 1968 [Mīkstie vāki]

  • Formāts: Paperback / softback, 144 pages, height x width: 235x155 mm, weight: 242 g, VIII, 144 p., 1 Paperback / softback
  • Sērija : Grundlehren der mathematischen Wissenschaften 148
  • Izdošanas datums: 01-Mar-2012
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642461263
  • ISBN-13: 9783642461262
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Introduction to Analytic Number Theory Softcover reprint of the original 1st ed. 1968Palielināt
  • Formāts: Paperback / softback, 144 pages, height x width: 235x155 mm, weight: 242 g, VIII, 144 p., 1 Paperback / softback
  • Sērija : Grundlehren der mathematischen Wissenschaften 148
  • Izdošanas datums: 01-Mar-2012
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642461263
  • ISBN-13: 9783642461262
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783642461262.html
Keywords:
This book has grown out of a course of lectures I have given at the Eidgenossische Technische Hochschule, Zurich. Notes of those lectures, prepared for the most part by assistants, have appeared in German. This book follows the same general plan as those notes, though in style, and in text (for instance, Chapters III, V, VIII), and in attention to detail, it is rather different. Its purpose is to introduce the non-specialist to some of the fundamental results in the theory of numbers, to show how analytical methods of proof fit into the theory, and to prepare the ground for a subsequent inquiry into deeper questions. It is pub­ lished in this series because of the interest evinced by Professor Beno Eckmann. I have to acknowledge my indebtedness to Professor Carl Ludwig Siegel, who has read the book, both in manuscript and in print, and made a number of valuable criticisms and suggestions. Professor Raghavan Narasimhan has helped me, time and again, with illuminating comments. Dr. Harold Diamond has read the proofs, and helped me to remove obscurities. I have to thank them all. K.C.

Papildus informācija

Springer Book Archives
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 Hurwitzs theorem.- §
1.
Approximation of irrationals.- §
2. Sums of two squares.- §
3. Primes of the
form 4k±.- §4. Hurwitzs theorem.- IV Quadratic residues and the
representation of a number as a sum of four squares.- §
1. The Legendre
symbol.- §
2. Wilsons theorem and Eulers 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 Möbius functions ?(n).- §
6. Eulers function ?(n).- VII Chebyshevs
therorem on the distribution of prime numbers.- §
1. The Chebyshev
functions.- §
2. Chebyshevs theorem.- §
3. Bertrands postulate.- §
4.
Eulers identity.- §
5. Some formulae of Mertens.- VIII Weyls theorems on
uniforms distribution and Kroneckers theorem.- §
1. Introduction.- §
2.
Uniform distribution in the unit interval.- §
3. Uniform distribution modulo
1.- §
4. Weyls theorems.- §
5. Kroneckers theorem.- IX Minkowskis theorem
on lattice points in convex sets.- §
1. Convex sets.- §
2. Minkowskis
theorem.- §
3. Applications.- XDirichlets theorem on primes in an
arithmetical progression.- §
1. Introduction.- §
2. Characters.- §
3. Sums of
characters, orthogonality relations.- §
4. Dirichlet series, Landaus
theorem.- §
5. Dirichlets 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.