Titlebook: Introduction to Cyclotomic Fields; Lawrence C. Washington Textbook 1997Latest edition Springer Science+Business Media New York 1997 Calc.C

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,The Kronecker—Weber Theorem,em is usually given as an easy consequence of class field theory. We do this in the Appendix. The main point is that in an abelian extension the splitting of primes is determined by congruence conditions, and we already know that . splits in . if . and only if mod ..

錢財(cái)

懶鬼才會(huì)衰弱

nonradioactive

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 riqng of integers and discriminant of. (ζ .). We start with the prime power case.

Intervention

擔(dān)心

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.

Biguanides

,The Second Case of Fermat’s Last Theorem,In Chapters 1 and 6 we treated the first case of Fermat’s Last Theorem, showing that there are no solutions provided certain conditions are satisfied by the class number.

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Introduction to Cyclotomic Fields978-1-4612-1934-7Series ISSN 0072-5285 Series E-ISSN 2197-5612