Abstract
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.
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References
Deitmar, A.: A First Course in Harmonic Analysis, 2nd edn. Universitext. Springer, New York (2005)
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© 2013 Springer-Verlag London
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Deitmar, A. (2013). p-Adic Numbers. In: Automorphic Forms. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-4435-9_4
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DOI: https://doi.org/10.1007/978-1-4471-4435-9_4
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4434-2
Online ISBN: 978-1-4471-4435-9
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