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

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Basic Results,In this chapter we prove some basic results on cyclotomic fields which will lay the groundwork for later chapters. We let ζ. denote a primitive .th root of unity. First we determine the ring of integers and discriminant of ℚ(ζ.). We start with the prime power case.

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Dirichlet ,-series and Class Number Formulas,In this chapter we review some of the basic facts about .-series. Then their values at negative integers are given in terms of generalized Bernoulli numbers. Finally, we discuss the values at 1 and relations with class numbers.

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,The Second Case of Fermat’s Last Theorem,by the class number. We now study the second case, namely.Again, the class number plays a role, but the units are also very important, which makes things much more difficult than in the first case. In fact, the second case is only known to hold for . < 125000, while the first case is known at present for . < 6 × 10..

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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.

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Textbook 19821st editionroup of the maximal unramified abelian extension is isomorphic to the ideal class group, and variants of this statement. The chapters are intended to be read consecutively, but it should be possible to vary the order considerably. The first four chapters are basic. After that, the reader willing to

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Lawrence C. Washingtonhe device‘s registers, to Driver Library, which provides a standardized set of application program interfaces (APIs) that enable software developers to quickly 978-3-031-79888-7978-3-031-79889-4Series ISSN 1932-3166 Series E-ISSN 1932-3174

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Lawrence C. Washingtonhe device‘s registers, to Driver Library, which provides a standardized set of application program interfaces (APIs) that enable software developers to quickly 978-3-031-79888-7978-3-031-79889-4Series ISSN 1932-3166 Series E-ISSN 1932-3174