Cyclotomic Fields I and II / Serge Lang / Buch / Graduate Texts in Mathematics / HC runder Rücken kaschiert / xvii / Englisch / 1989 / Springer US / EAN 9780387966717 - encadernado, livro de bolso
1989, ISBN: 9780387966717
[ED: Gebunden], [PU: Springer US], Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, … mais…
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Cyclotomic Fields I and II | Serge Lang | Buch | Graduate Texts in Mathematics | HC runder Rücken kaschiert | xvii | Englisch | 1989 | Springer US | EAN 9780387966717 - encadernado, livro de bolso
1989, ISBN: 9780387966717
[ED: Gebunden], [PU: Springer US], Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, … mais…
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Cyclotomic Fields I and II (Graduate Texts in Mathematics, 121, Band 121) - encadernado, livro de bolso
1989, ISBN: 9780387966717
Assistent: Rubin, Karl, Springer, Gebundene Ausgabe, Auflage: 2nd ed. 1990, 453 Seiten, Publiziert: 1989-12-18T00:00:01Z, Produktgruppe: Buch, 3.99 kg, Verkaufsrang: 2828167, Algebra & Za… mais…
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1989, ISBN: 9780387966717
[ED: Gebunden], [PU: Springer New York], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Kummer s work on cyclotomic fields paved the way … mais…
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1989, ISBN: 0387966714
2nd ed. 1990 Gebundene Ausgabe Zahlentheorie, Prime; Algebra; finitefield; homomorphism; numbertheory; cohomology, mit Schutzumschlag 11, [PU:Springer New York; Springer US]
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Cyclotomic Fields I and II / Serge Lang / Buch / Graduate Texts in Mathematics / HC runder Rücken kaschiert / xvii / Englisch / 1989 / Springer US / EAN 9780387966717 - encadernado, livro de bolso
1989, ISBN: 9780387966717
[ED: Gebunden], [PU: Springer US], Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, … mais…
Lang, Serge:
Cyclotomic Fields I and II | Serge Lang | Buch | Graduate Texts in Mathematics | HC runder Rücken kaschiert | xvii | Englisch | 1989 | Springer US | EAN 9780387966717 - encadernado, livro de bolso1989, ISBN: 9780387966717
[ED: Gebunden], [PU: Springer US], Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, … mais…
Cyclotomic Fields I and II (Graduate Texts in Mathematics, 121, Band 121) - encadernado, livro de bolso
1989
ISBN: 9780387966717
Assistent: Rubin, Karl, Springer, Gebundene Ausgabe, Auflage: 2nd ed. 1990, 453 Seiten, Publiziert: 1989-12-18T00:00:01Z, Produktgruppe: Buch, 3.99 kg, Verkaufsrang: 2828167, Algebra & Za… mais…
1989, ISBN: 9780387966717
[ED: Gebunden], [PU: Springer New York], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Kummer s work on cyclotomic fields paved the way … mais…
1989, ISBN: 0387966714
2nd ed. 1990 Gebundene Ausgabe Zahlentheorie, Prime; Algebra; finitefield; homomorphism; numbertheory; cohomology, mit Schutzumschlag 11, [PU:Springer New York; Springer US]
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Dados detalhados do livro - Cyclotomic Fields I and II (Graduate Texts in Mathematics, 121, Band 121)
EAN (ISBN-13): 9780387966717
ISBN (ISBN-10): 0387966714
Livro de capa dura
Livro de bolso
Ano de publicação: 2007
Editor/Editora: Springer
458 Páginas
Peso: 0,877 kg
Língua: eng/Englisch
Livro na base de dados desde 2007-05-28T13:44:13+01:00 (Lisbon)
Página de detalhes modificada pela última vez em 2024-02-04T14:33:54+00:00 (Lisbon)
Número ISBN/EAN: 9780387966717
Número ISBN - Ortografia alternativa:
0-387-96671-4, 978-0-387-96671-7
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Autor do livro: karl lang, serge lang
Título do livro: graduate texts mathematics, the fields, cyclotomic fields and
Dados da editora
Autor: Serge Lang
Título: Graduate Texts in Mathematics; Cyclotomic Fields I and II
Editora: Springer; Springer US
436 Páginas
Ano de publicação: 1989-12-18
New York; NY; US
Língua: Inglês
90,94 € (DE)
93,49 € (AT)
100,50 CHF (CH)
Available
XVII, 436 p.
BB; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Zahlentheorie; Verstehen; Cohomology; Prime; algebra; finite field; homomorphism; number theory; Number Theory; BC
1 Character Sums.- 1. Character Sums over Finite Fields.- 2. Stickelberger’s Theorem.- 3. Relations in the Ideal Classes.- 4. Jacobi Sums as Hecke Characters.- 5. Gauss Sums over Extension Fields.- 6. Application to the Fermat Curve.- 2 Stickelberger Ideals and Bernoulli Distributions.- 1. The Index of the First Stickelberger Ideal.- 2. Bernoulli Numbers.- 3. Integral Stickelberger Ideals.- 4. General Comments on Indices.- 5. The Index for k Even.- 6. The Index for k Odd.- 7. Twistings and Stickelberger Ideals.- 8. Stickelberger Elements as Distributions.- 9. Universal Distributions.- 10. The Davenport-Hasse Distribution.- Appendix. Distributions.- 3 Complex Analytic Class Number Formulas.- 1. Gauss Sums on Z/mZ.- 2. Primitive L-series.- 3. Decomposition of L-series.- 4. The (± 1)-eigenspaces.- 5. Cyclotomic Units.- 6. The Dedekind Determinant.- 7. Bounds for Class Numbers.- 4 The p-adic L-function.- 1. Measures and Power Series.- 2. Operations on Measures and Power Series.- 3. The Mellin Transform and p-adic L-function.- Appendix. The p-adic Logarithm.- 4. The p-adic Regulator.- 5. The Formal Leopoldt Transform.- 6. The p-adic Leopoldt Transform.- 5 Iwasawa Theory and Ideal Class Groups.- 1. The Iwasawa Algebra.- 2. Weierstrass Preparation Theorem.- 3. Modules over ZP[[X]].- 4. Zp-extensions and Ideal Class Groups.- 5. The Maximal p-abelian p-ramified Extension.- 6. The Galois Group as Module over the Iwasawa Algebra.- 6 Kummer Theory over Cyclotomic Zp-extensions.- 1. The Cyclotomic Zp-extension.- 2. The Maximal p-abelian p-ramified Extension of the Cyclotomic Zp-extension.- 3. Cyclotomic Units as a Universal Distribution.- 4. The Iwasawa-Leopoldt Theorem and the Kummer-Vandiver Conjecture.- 7 Iwasawa Theory of Local Units.- 1. The Kummer-Takagi Exponents.- 2.Projective Limit of the Unit Groups.- 3. A Basis for U(x) over A.- 4. The Coates-Wiles Homomorphism.- 5. The Closure of the Cyclotomic Units.- 8 Lubin-Tate Theory.- 1. Lubin-Tate Groups.- 2. Formal p-adic Multiplication.- 3. Changing the Prime.- 4. The Reciprocity Law.- 5. The Kummer Pairing.- 6. The Logarithm.- 7. Application of the Logarithm to the Local Symbol.- 9 Explicit Reciprocity Laws.- 1. Statement of the Reciprocity Laws.- 2. The Logarithmic Derivative.- 3. A Local Pairing with the Logarithmic Derivative.- 4. The Main Lemma for Highly Divisible x and ? = xn.- 5. The Main Theorem for the Symbol ?x, xn?n.- 6. The Main Theorem for Divisible x and ? = unit.- 7. End of the Proof of the Main Theorems.- 10 Measures and Iwasawa Power Series.- 1. Iwasawa Invariants for Measures.- 2. Application to the Bernoulli Distributions.- 3. Class Numbers as Products of Bernoulli Numbers.- Appendix by L. Washington: Probabilities.- 4. Divisibility by l Prime to p: Washington’s Theorem.- 11 The Ferrero-Washington Theorems.- 1. Basic Lemma and Applications.- 2. Equidistribution and Normal Families.- 3. An Approximation Lemma.- 4. Proof of the Basic Lemma.- 12 Measures in the Composite Case.- 1. Measures and Power Series in the Composite Case.- 2. The Associated Analytic Function on the Formal Multiplicative Group.- 3. Computation of Lp(1, x) in the Composite Case.- 13 Divisibility of Ideal Class Numbers.- 1. Iwasawa Invariants in Zp-extensions.- 2. CM Fields, Real Subfields, and Rank Inequalities.- 3. The l-primary Part in an Extension of Degree Prime to l.- 4. A Relation between Certain Invariants in a Cyclic Extension.- 5. Examples of Iwasawa.- 6. A Lemma of Kummer.- 14 P-adic Preliminaries.- 1. The p-adic Gamma Function.- 2. The Artin-Hasse Power Series.- 3. AnalyticRepresentation of Roots of Unity.- Appendix: Barsky’s Existence Proof for the p-adic Gamma Function.- 15 The Gamma Function and Gauss Sums.- 1. The Basic Spaces.- 2. The Frobenius Endomorphism.- 3. The Dwork Trace Formula and Gauss Sums.- 4. Eigenvalues of the Frobenius Endomorphism and the p-adic Gamma Function.- 5. p-adic Banach Spaces.- 16 Gauss Sums and the Artin-Schreier Curve.- 1. Power Series with Growth Conditions.- 2. The Artin-Schreier Equation.- 3. Washnitzer-Monsky Cohomology.- 4. The Frobenius Endomorphism.- 17 Gauss Sums as Distributions.- 1. The Universal Distribution.- 2. The Gauss Sums as Universal Distributions.- 3. The L-function at s = 0.- 4. The p-adic Partial Zeta Function.- Appendix by Karl Rubin.- The Main Conjecture.- 1. Setting and Notation.- 2. Properties of Kolyvagin’s “Euler System”.- 3. An Application of the Chebotarev Theorem.- 5. The Main Conjecture.- 6. Tools from Iwasawa Theory.- 7. Proof of Theorem 5.1.- 8. Other Formulations and Consequences of the Main Conjecture.Outros livros adicionais, que poderiam ser muito similares com este livro:
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