1 also include two proofs of the functional equation for the zeta function, to acquaint the reader with different techniques (in some sense equivalent, but in another sense, suggestive of very different moods). Stylistically, 1 have intermingled the ideal and idelic approaches without prejudice for either. There is much to be said for a direct global approach to number fields. For a more complete treatment of these, cf. It is the only source I know with a detailed approach to the proof of the main global theorem via zeta functions. Lecturer: zlem Imamoglu Coordinator: Emilio Corso Room: HG G 19.1, except for 23/09 and 11/11.
The point of view taken here is principally global, and we deal with local fields only incidentally. It gives a cohomological treatment of class field theory without every saying the words, which is both a bug and a feature. Student Seminar in Elementary Number Theory Autumn 2021.
Old, and seemingly isolated special cases have continuously acquired renewed significance, often after half a century or more. 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.
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 W eber, Hasse, Hecke, and Hilbert's Zahlbericht. the class field theory on which 1 make further comments at the appropriate place later. 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. Springer : : 340 : USD 69.95 : Hardcover : Undergraduate Texts in Mathematics.
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