p-Adic Numbers

  • Anton Deitmar
Part of the Universitext book series (UTX)


For a prime number p, the field of p-adic numbers is a completion of the field of rationals. Together with the field of reals, the p-adic numbers form all completions of ℚ. In this chapter we discuss the notion of absolute values on fields and their completions. We give several useful descriptions of the field ℚ p of p-adic numbers and compute the additive and multiplicative Haar-measures, which are the equivalents of the Lebesgue measure in the case of the real numbers.


  1. [Dei05]
    Deitmar, A.: A First Course in Harmonic Analysis, 2nd edn. Universitext. Springer, New York (2005) Google Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Anton Deitmar
    • 1
  1. 1.Inst. MathematikUniversität TübingenTübingenGermany

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