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

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-Series AgainLet . be a character of the idele classes . (or equivalently, of ., vanishing on .*), that is a continuous homomorphism./.* → C*,.. Then the kernel . of . is a closed subgroup of finite index, which is therefore open, and has a class field denoted by ..

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Functional Equation, Tate’s ThesisThis chapter is essentially Tate’s thesis, which has also appeared (finally) in the Brighton conference volume.

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The Brauer-Siegel TheoremUsing the integrals expressing the zeta function, one can give certain estimates concerning its residue in order to derive asymptotic results relating the class number, regulator, and discriminant of a number field, and notably the following.

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Graduate Texts in Mathematicshttp://image.papertrans.cn/a/image/152687.jpg

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