Titlebook: Introduction to Cyclotomic Fields; Lawrence C. Washington Textbook 19821st edition Springer-Verlag New York Inc. 1982 Fields.Kreisk?rper.a

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Mosaic

paltry

流浪

Cyclotomic Units,e explicitly a group of units, namely the cyclotomic units, which is of finite index in the full unit group. Moreover, this index is closely related to the class number, a fact which allows us to prove Leopoldt’s .-adic class number formula. Finally, we study more closely the units of the .th cyclot

cloture

Locale

Galois Groups Acting on Ideal Class Groups,o great advantage to reinterpret old results and to obtain new information on the structure of class groups. In this chapter we first give some results which are useful when working with class groups and class numbers. We then present the basic machinery, essentially Leopoldt’s Spiegelungsatz, which

墻壁

Cyclotomic Fields of Class Number One,y finitely many such fields, but the result was noneffective: there was no computable bound on .. So we need other techniques. Since . divides . if . divides ., it is reasonable to start with . prime. In 1964 Siegel showed that . = 1 implies . ≤ ., where . is a computable constant, but the constant

Dappled

Measures and Distributions,As we shall see, many ideas from Chapters 4, 5, 7, and 8 fit into this general framework. The related concept of a measure yields a .-adic integration theory which allows us to interpret the .-adic .-function as a Mellin transform, as in the classical case.

傀儡

鬧劇

The Kronecker-Weber Theorem, in 1853, but his proof was incomplete. In particular, there were difficulties with extensions of degree a power of 2. Even in the proof we give below this case requires special consideration. The first proof was given by Weber in 1886 (there was still a gap; see Neumann [1]). Both Kronecker and Web