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

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https://doi.org/10.1007/978-981-16-3957-9Let . be a function on .. We shall say that . . if for each positive integer . the function.is bounded for |.| sufficiently large.

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https://doi.org/10.1007/978-981-16-3957-9This chapter is essentially Tate’s thesis, which has also appeared (finally) in the Brighton conference volume.

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Algebraic IntegersThis chapter describes the basic aspects of the ring of algebraic integers in a number field (always assumed to be of finite degree over the rational numbers .). This includes the general prime ideal structure.

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The Different and DiscriminantThe study of the different and discriminant provides some information on ramified primes, and also gives a sort of duality which plays a role both in the algebraic study of ramification and the later chapters on analytic duality. It also gives a good method for computing the ring of algebraic integers in a number field, as in Proposition 10.

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ParallelotopesThis chapter gives quantitative results concerning the distribution of elements of a number field in parallelotopes.