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Introduction to Cyclotomic Fields 2nd ed. 1997 [Kõva köide]

  • Formaat: Hardback, 490 pages, kõrgus x laius: 235x155 mm, kaal: 1950 g, XIV, 490 p., 1 Hardback
  • Sari: Graduate Texts in Mathematics 83
  • Ilmumisaeg: 05-Dec-1996
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 0387947620
  • ISBN-13: 9780387947624
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Introduction to Cyclotomic Fields 2nd ed. 1997Suurem pilt
  • Formaat: Hardback, 490 pages, kõrgus x laius: 235x155 mm, kaal: 1950 g, XIV, 490 p., 1 Hardback
  • Sari: Graduate Texts in Mathematics 83
  • Ilmumisaeg: 05-Dec-1996
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 0387947620
  • ISBN-13: 9780387947624
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780387947624.html
Märksõnad:
Introduction to Cyclotomic Fields is a carefully written exposition of a central area of number theory that can be used as a second course in algebraic number theory. Starting at an elementary level, the volume covers p-adic L-functions, class numbers, cyclotomic units, Fermat's Last Theorem, and Iwasawa's theory of Z[ subscript p]-extensions, leading the reader to an understanding of modern research literature. Many exercises are included.
The second edition includes a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture. There is also a chapter giving other recent developments, including primality testing via Jacobi sums and Sinnott's proof of the vanishing of Iwasawa's [ mu]-invariant.

Introduction to Cyclotomic Fields is a carefully written exposition of a central area of number theory that can be used as a second course in algebraic number theory. Starting at an elementary level, the volume covers p-adic L-functions, class numbers, cyclotomic units, Fermat's Last Theorem, and Iwasawa's theory of Z_p-extensions, leading the reader to an understanding of modern research literature. Many exercises are included. The second edition includes a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture. There is also a chapter giving other recent developments, including primality testing via Jacobi sums and Sinnott's proof of the vanishing of Iwasawa's f-invariant.

This text on a central area of number theory covers p-adic L-functions, class numbers, cyclotomic units, Fermat's Last Theorem, and Iwasawa's theory of Z_p-extensions. This edition contains a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture, as well as a chapter on other recent developments, such as primality testing via Jacobi sums and Sinnott's proof of the vanishing of Iwasawa's f-invariant.

Muu info

Springer Book Archives
1 Fermats Last Theorem.- 2 Basic Results.- 3 Dirichlet Characters.- 4
Dirichlet L-series and Class Number Formulas.- 5 p-adic L-functions and
Bernoulli Numbers.- 5.1. p-adic functions.- 5.2. p-adic L-functions.- 5.3.
Congruences.- 5.4. The value at s = 1.- 5.5. The p-adic regulator.- 5.6.
Applications of the class number formula.- 6 Stickelbergers Theorem.- 6.1.
Gauss sums.- 6.2. Stickelbergers theorem.- 6.3. Herbrands theorem.- 6.4.
The index of the Stickelberger ideal.- 6.5. Fermats Last Theorem.- 7
Iwasawas Construction of p-adic L-functions.- 7.1. Group rings and power
series.- 7.2. p-adic L-functions.- 7.3. Applications.- 7.4. Function fields.-
7.5. µ = 0.- 8 Cyclotomic Units.- 8.1. Cyclotomic units.- 8.2. Proof of the
p-adic class number formula.- 8.3. Units of
$$
\mathbb{Q}\left( {{\zeta _p}} \right)$$
and Vandivers conjecture.- 8.4. p-adic expansions.- 9 The Second Case of
Fermats Last Theorem.- 9.1. The basic argument.- 9.2. The theorems.- 10
Galois Groups Acting on Ideal Class Groups.- 10.1. Some theorems on class
groups.- 10.2. Reflection theorems.- 10.3. Consequences of Vandivers
conjecture.- 11 Cyclotomic Fields of Class Number One.- 11.1. The estimate
for even characters.- 11.2. The estimate for all characters.- 11.3. The
estimate for hm-.- 11.4. Odlyzkos bounds on discriminants.- 11.5.
Calculation of hm+.- 12 Measures and Distributions.- 12.1. Distributions.-
12.2. Measures.- 12.3. Universal distributions.- 13 Iwasawas Theory of
$$
{\mathbb{Z}_p} -$$
extensions.- 13.1. Basic facts.- 13.2. The structure of A-modules.- 13.3.
Iwasawas theorem.- 13.4. Consequences.- 13.5. The maximal abelian
p-extension unramified outside p.- 13.6. The main conjecture.- 13.7.
Logarithmic derivatives.- 13.8. Local units modulo cyclotomicunits.- 14 The
KroneckerWeber Theorem.- 15 The Main Conjecture and Annihilation of Class
Groups.- 15.1. Stickelbergers theorem.- 15.2. Thaines theorem.- 15.3. The
converse of Herbrands theorem.- 15.4. The Main Conjecture.- 15.5. Adjoints.-
15.6. Technical results from Iwasawa theory.- 15.7. Proof of the Main
Conjecture.- 16 Miscellany.- 16.1. Primality testing using Jacobi sums.-
16.2. Sinnotts proof that µ = 0.- 16.3. The non-p-part of the class number
in a
$$
{\mathbb{Z}_p} -$$
extension.-
1. Inverse limits.-
2. Infinite Galois theory and ramification
theory.-
3. Class field theory.- Tables.-
1. Bernoulli numbers.-
2. Irregular
primes.-
3. Relative class numbers.-
4. Real class numbers.- List of Symbols.