代数数论 第2版（影印版）

.chapter iii
the different and discriminant
1. complementary modules
2. the different and ramification
3. the discriminant
chapter iv
cyclotomic fields
1. roots of unity
2. quadratic fields
3. gauss sums
4. relations in ideal classes
charter v
parallelotopes
1. the product formula
2. lattice points in parallelotopes
3. a volume computation
4. minkowski's constant
chapter vi
the ideal function
1. generalized ideal classes
2. lattice points in homogeneously expanding domains
3. the number of ideals in a given class
chapter vii
ideles and adeles
1. restricted direct products
2. adeles
3. ideles
4. generalized ideal class groups; relations with idele classes
5. embedding of k* in the idele classes
6. galois operation on ideles and idele classes
chapter viii
elementary properties of the zeta function and l-series
1. lemmas on dirichlet series
2. zeta function of a number field
3. the l-series
4. density of primes in arithmetic progressions
5. farings' finiteness theorem
part two
class field theory
chapter ix
norm index computations
1. algebraic preliminaries
2. exponential and logarithm functions
3. the local norm index
4. a theorem on units
5. the global cyclic norm index
6. applications
chapter x
the artin symbol, reciprocity law, and class field theory
1. formalism of the artin symbol
2. existence of a conductor for the artin symbol
3. class fields
chapter xi
the existence theorem and local class field theory
1. reduction to kummer extensions
2. proof of the existence theorem
3. the complete splitting theorem
4. local class field theory and the ramification theorem
5. the hilbert class field and the principal ideal theorem
6. infinite divisibility of the universal norms
chapter xii
l-series again
1. the proper abelian l-series
2. artin (non-abelian) l-series
3. induced characters and l-series contributions
part three
analytic theory
charter xiii
functional equation of the zeta function, hecke's proof
1. the poisson summation formula
2. a special computation
3. functional equation
4. application to the brauer-siegel theorem
5. applications to the ideal function
appendix: other applications
charter xiv
functional equation, tate's thesis
1. local additive duality
2. local multiplicative theory
3. local functional equation
4. local computations
5. restricted direct products
6. global additive duality and riemann-roch theorem
7. global functional equation
8. global computations
chapter xv
density of primes and tauberian theorem
1. the dirichlet integral
2. ikehara's tauberian theorem
3. tauberian theorem for dirichlet series
4. non-vanishing of the l-series
5. densities
chapter xvi
the brauer-siegel theorem
1. an upper estimate for the residue
2. a lower bound for the residue
3. comparison of residues in normal extensions
4. end of the proofs
appendix: brauer's lemma
chapter xvii
explicit formulas
1. weierstrass factorization of the l-series
2. an estimate for
3. the well formula
4. the basic sum and the first part of its evaluation
5. evaluation of the sum: second part
bibliography
index