Cyclotomic Fields II

Graduate Texts in Mathematics #69

by Serge A. Lang

Volume II.- 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. Probabilities.- 4. Divisibility by l Prime to 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(l, 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. Analytic Representation of Roots of Unity.- 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.

180 pages, Paperback

First published May 1, 1980