Böcker av S. 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. 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(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.- 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.

SL2(R) gives the student an introduction to the infinite dimensional representation theory of semisimple Lie groups by concentrating on one example - SL2(R). The rapid development of representation theory over the past 40 years has made it increasingly difficult for a student to enter the field.

The book describes the effects of natural as well as artificial electromagnetic energies covering the en tire measurable frequency range from the highest frequencies, x-rays, through microwaves, radio waves, and finally extremely low frequency (ELF) waves.

In the present book, we have put together the basic theory of the units and cuspidal divisor class group in the modular function fields, developed over the past few years. Then r(N)\i) 2 is complex analytic isomorphic to an affine curve YeN), whose compactifi cation is called the modular curve X(N).