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Titlebook: Algebraic Number Theory; Serge Lang Textbook 19861st edition Springer Science+Business Media New York 1986 algebraic number theory.analyti

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樓主
發(fā)表于 2025-3-21 16:56:09 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
期刊全稱Algebraic Number Theory
影響因子2023Serge Lang
視頻videohttp://file.papertrans.cn/153/152687/152687.mp4
學(xué)科分類Graduate Texts in Mathematics
圖書封面Titlebook: Algebraic Number Theory;  Serge Lang Textbook 19861st edition Springer Science+Business Media New York 1986 algebraic number theory.analyti
影響因子The present book gives an exposition of the classical basic algebraic and analytic number theory and supersedes my Algebraic Numbers, including much more material, e. g. the class field theory on which I make further comments at the appropriate place later. For different points of view, the reader is encouraged to read the collec- tion of papers from the Brighton Symposium (edited by Cassels-Frohlich), the Artin-Tate notes on class field theory, Weil‘s book on Basic Number Theory, Borevich-Shafarevich‘s Number Theory, and also older books like those of Weber, Hasse, Hecke, and Hilbert‘s Zahlbericht. It seems that over the years, everything that has been done has proved useful, theo- retically or as examples, for the further development of the theory. Old, and seemingly isolated special cases have continuously acquired renewed significance, often after half a century or more. The point of view taken here is principally global, and we deal with local fields only incidentally. For a more complete treatment of these, cf. Serre‘s book Corps Locaux. There is much to be said for a direct global approach to number fields. Stylistically, I have intermingled the ideal and idelic approaches w
Pindex Textbook 19861st edition
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沙發(fā)
發(fā)表于 2025-3-21 21:22:45 | 只看該作者
The Ideal Function fractional ideals (which we say from now on, instead of non-zero ideals, unless otherwise specified), then we write a ~ b (a is equivalent to b) if there exists α ? . such that a = (α)b, i.e. ab. is a principal fractional ideal. Then the equivalence classes of fractional ideals form a finite group
板凳
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地板
發(fā)表于 2025-3-22 06:59:08 | 只看該作者
The Existence Theorem and Local Class Field Theorytensions of .. There are not that many ways of doing this. One general way is to make cyclotomic extensions, and when the n-th roots of unity are in ., to make Kummer extensions, i.e. adjoining .-th roots of elements of .. We shall prove the existence theorem by this method. Deeper methods involving
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發(fā)表于 2025-3-22 22:52:45 | 只看該作者
Classifying and Modeling IoT Behavior,here exists α ? . such that a = (α)b, i.e. ab. is a principal fractional ideal. Then the equivalence classes of fractional ideals form a finite group (as we saw in Chapter V, §1), which we call the .. Its order is usually denoted by ., and is called the. of ..
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發(fā)表于 2025-3-23 04:17:44 | 只看該作者
Defending the American Presidency, to make Kummer extensions, i.e. adjoining .-th roots of elements of .. We shall prove the existence theorem by this method. Deeper methods involving the values of certain transcendental functions are more significant, but lead into directions which require a whole book to themselves. We first start with the reduction lemma.
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發(fā)表于 2025-3-23 07:12:27 | 只看該作者
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