Titlebook: p-adic Numbers; An Introduction Fernando Q. Gouvêa Textbook 19931st edition Springer-Verlag Berlin Heidelberg 1993 Rack.calculus.completion

使饥饿

Myocyte

,Apéritif,t arise merely from some desire to generalize, but rather from several concrete situations involving problems from algebra and number theory. The new “metrics” on ℚ will be each connected to a certain prime, and they will “codify” a great deal of arithmetic information related to that prime. The goa

小歌剧

ANTIC

obviate

,Elementary Analysis in ℚ,,d it is complete with respect to the metric given by that absolute value. In fact, the similarities go deeper: ℝ and the various ℚ., are completions of ℚ, hence contain ℚ as a dense subset; they are all locally compact; none of them are algebraically closed.

Offbeat

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,Analysis in ℂ,,his book, we try to touch on a few remarkable points: the theory of Newton polygons, the .-adic Weierstrass Preparation Theorem, the description of entire functions. As usual, the first step is to re-appropriate all the results we obtained earlier. We then go on to consider how to extend the .-adic

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Introduction,rners of mathematics. The goal of this book is to offer such an opportunity, by way of a visit to the .-adic universe. Such a visit offers a glimpse of a part of mathematics which is both important and fun, and which also is something of a meeting point between algebra and analysis.

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0172-5939 ck. Those who will later specialize in number theory,algebraic geometry, and related subjects will benefit moredirectly, but all mathematics students can enjoy the book.978-3-662-22278-2Series ISSN 0172-5939 Series E-ISSN 2191-6675