Author | Washington, Lawrence C. author |
---|---|
Title | Introduction to Cyclotomic Fields [electronic resource] / by Lawrence C. Washington |
Imprint | New York, NY : Springer US, 1982 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0133-2 |
Descript | online resource |
1 Fermatโs Last Theorem -- 2 Basic Results -- 3 Dirichlet Characters -- 4 Dirichlet L-series and Class Number Formulas -- 5 p-adic L-funetions and Bernoulli Numbers -- 5.1. p-adic functions -- 5.2. p-adic L-functions -- 5.3. Congruences -- 5.4. The value at s = 1 -- 5.5. Thep-adic regulator -- 5.6. Applications of the class number formula -- 6 Stickelbergerโs Theorem -- 6.1. Gauss sums -- 6.2. Stickelbergerโs theorem -- 6.3. Herbrandโs theorem -- 6.4. The index of the Stiekelberger ideal -- 6.5. Fermatโs Last Theorem -- 7 Iwasawaโs Construction of p-adic L-functions -- 7.1. Group rings and power series -- 7.2. p-adic L-functions -- 7.3. Applications -- 7.4. Function fields -- 7.5. ? = 0 -- 8 Cyclotomic Units -- 8.1. Cyclotomic units -- 8.2. Proof of the p-adic class number formula -- 8.3. Units of ?(?p) and Vandiverโs conjecture -- 8.4. p-adic expansions -- 9 The Second Case of Fermatโs Last Theorem -- 9.1. The basic argument -- 9.2. The theorems -- 10 Galois Groups Acting on Ideal Class Groups -- 10.1. Some theorems on class groups -- 10.2. Reflection theorems -- 10.3. Consequences of Vandiverโs conjecture -- 11 Cyclotomic Fields of Class Number One -- 11.1. The estimate for even characters -- 11.2. The estimate for all characters -- 11.3. The estimate for hm? -- 11.4. Odlyzkoโs bounds on discriminants -- 11.5. Calculation of hm+ -- 12 Measures and Distributions -- 12.1. Distributions -- 12.2. Measures -- 12.3. Universal distributions -- 13 Iwasawaโs Theory of ?p-extensions -- 13.1. Basic facts -- 13.2. The structure of ?-modules -- 13.3. Iwasawaโs theorem -- 13.4. Consequences -- 13.5. The maximal abelian p-extension unramified outside p -- 13.6. The main conjecture -- 13.7. Logarithmic derivatives -- 13.8. Local units modulo cyclotomic units -- 14 The Kronecker-Weber Theorem -- Tables -- List of Symbols