Algebraic Number TheorySpringer Science & Business Media, 6 dic 2012 - 269 pagine From the reviews: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995 |
Dall'interno del libro
Risultati 1-5 di 69
Pagina 2
... Subgroups of J ( K ) / K * of Finite Index and the Ray Class Groups §6 . Hecke L - Series and the Distribution of Prime Ideals 6.1 . The Local Zeta Functions 6.2 . The Global Functional Equation 6.3 . Hecke Characters 6.4 . The ...
... Subgroups of J ( K ) / K * of Finite Index and the Ray Class Groups §6 . Hecke L - Series and the Distribution of Prime Ideals 6.1 . The Local Zeta Functions 6.2 . The Global Functional Equation 6.3 . Hecke Characters 6.4 . The ...
Pagina 10
... subgroup of K. Since the group K✶ has no torsion , m is a free Z - module of rank < [ K : Q ] . The module m is called complete ( or a lattice in K ) if its rank is equal to [ K : Q ] . Modules play an important role in the arithmetic ...
... subgroup of K. Since the group K✶ has no torsion , m is a free Z - module of rank < [ K : Q ] . The module m is called complete ( or a lattice in K ) if its rank is equal to [ K : Q ] . Modules play an important role in the arithmetic ...
Pagina 15
... ) From Lemma 1.14 it follows also that ( 0 * ) is a discrete subgroup of U , and since the vector space U has dimension r rank < r - 1 . ----- d ) For the proof of Theorem 1.13 it remains § 1. Orders in Algebraic Number Fields 15 15.
... ) From Lemma 1.14 it follows also that ( 0 * ) is a discrete subgroup of U , and since the vector space U has dimension r rank < r - 1 . ----- d ) For the proof of Theorem 1.13 it remains § 1. Orders in Algebraic Number Fields 15 15.
Pagina 19
... subgroup of * of index 1 or 2. This index is called the unit index . If K has no real conjugate then of course every unit has norm 1. In general no simple criterion is known for the determination of the unit index.☐ Example 7. Let K ...
... subgroup of * of index 1 or 2. This index is called the unit index . If K has no real conjugate then of course every unit has norm 1. In general no simple criterion is known for the determination of the unit index.☐ Example 7. Let K ...
Pagina 20
... subgroup H ( O ) of M ( O ) , and CL ( O ) can be identified with the factor group M ( O ) / H ( O ) . We want to connect the set of classes of binary quadratic forms with CL ( D ) . We have already associated with a module m an ...
... subgroup H ( O ) of M ( O ) , and CL ( O ) can be identified with the factor group M ( O ) / H ( O ) . We want to connect the set of classes of binary quadratic forms with CL ( D ) . We have already associated with a module m an ...
Sommario
7 | |
22 | |
3 Dedekind Rings | 28 |
60 | 42 |
69 | 49 |
76 | 56 |
Harmonic Analysis on Local and Global Fields | 63 |
6 Hecke LSeries and the Distribution of Prime Ideals | 70 |
7 Further Results of Class Field Theory | 145 |
Cohomology of Profinite Groups | 151 |
2 Galois Cohomology of Local and Global Fields | 168 |
Abelian Fields | 192 |
3 Iwasawas Theory of IExtensions | 206 |
Artin LFunctions and Galois Module Structure | 219 |
2 Galois Module Structure and Artin Root Numbers | 234 |
Fields Domains and Complexes | 237 |
Class Field Theory | 90 |
2 Complex Multiplication | 107 |
Simple Algebras | 131 |
6 Explicit Reciprocity Laws and Symbols | 137 |
Tables | 245 |
References | 251 |
Author Index 263 | 262 |
Altre edizioni - Visualizza tutto
Parole e frasi comuni
a₁ abelian extension abelian field abelian group algebraic number field arbitrary Artin automorphism called Chap class field theory closed subgroup cohomology complex conductor conjecture corresponding cyclic Dedekind ring defined denotes Dirichlet discriminant divisor theory exact sequence Example extension L/K extension of Q finite extension finite group finite normal extension following theorem function G-module G₁ Galois group global fields group G H¹(G H²(G Hasse Hecke character Hence Hilbert homomorphism ideal class group idele imaginary-quadratic implies induces infinite places integers irreducible isomorphism L-functions Lemma Let G Let L/K Main reference module morphism natural number norm symbol normal extension normal subgroup number theory polynomial prime divisors prime element prime ideal prime numbers principal ideal pro-p-group profinite group Proposition quadratic r₂ ramified reciprocity law representation resp roots of unity Shafarevich simple algebra subgroup of G trivial U₁ unramified valuation Z/pZ