Titlebook: p-adic Numbers, p-adic Analysis, and Zeta-Functions; Neal Koblitz Textbook 1984Latest edition Springer Science+Business Media New York 198

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978-1-4612-7014-0Springer Science+Business Media New York 1984

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-adic numbers,If . is a nonempty set, a distance, or ., on . is a function . from pairs of elements (., .) of . to the nonnegative real numbers such that.A set . together with a metric . is called a .. The same set . can give rise to many different metric spaces (.), as we’ll soon see.

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,Building up Ω,In what follows, we’ll have to assume familiarity with a few basic notions concerning algebraic extensions of fields. It would take us too far afield to review all the proofs; for a complete and readable treatment, see Lang’s . or Herstein’s ..