Abstract
We study an injective embedding of p-adic integers in the Cartesian product of p copies of sets of 2-adic integers. This embedding allows to explicitly specify any p-adic integer through p specially selected 2-adic numbers. This representation can be used in p-adic mathematical physics, for example, in justifying choice of the parameter p.
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References
S. Albeverio, A. Khrennikov, B. Tirozzi, D. De Smedt, p-adic dynamical systems. Theor. Math. Phys. 114, 276–287 (1998)
V. Anashin, A. Khrennikov, Applied Algebraic Dynamics. de Gruyter Expositions in Mathematics, vol. 49 (Walter de Gruyter, Berlin, 2009)
D.K. Arrowsmith, F. Vivaldi, Geometry of p-adic Siegel discs. Phys. D 71, 222–236 (1994)
B. Dragovich, A. Khrennikov, S.V. Kozyrev, I.V. Volovich, On p-adic mathematical physics. P-Adic Numbers Ultrametric Anal. Appl. 1, 1–17 (2009)
M.S. El Naschie, P-Adic unification of the fundamental forces and the standard model. Chaos, Solitons Fractals 38, 1011–1012 (2008)
A.Y. Khrennikov, P-adic Valued Distributions in Mathematical Physics (Kluwer, Dordrecht, 1994)
A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models (Kluwer, Dordrecht, 1997)
A. Khrennikov, E. Yurova, Criteria of ergodicity for p-adic dynamical systems in terms of coordinate functions. Chaos, Solitons Fractals 60, 11–30 (2014)
K. Mahler, P-adic Numbers and Their Functions (Cambridge University Press, London, 1981)
W.H. Schikhof, Ultrametric Calculus. An Introduction to p-Adic Analysis (Cambridge University Press, Cambridge, 984)
F. Vivaldi, The arithmetic of discretized rotations, in AIP Conference Proceedings on P-adic Mathematical Physics, vol. 826, ed. by A.Y. Khrennikov, Z. Rakic, I.V. Volovich (Melville, New York, 2006), pp. 162–173
V.S. Vladimirov, I.V. Volovich, E.I. Zelenov, P-adic Analysis and Mathematical Physics (World Scientific, Singapore, 1994)
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Axelsson, E.Y. (2019). On the Injective Embedding of p-Adic Integers in the Cartesian Product of p Copies of Sets of 2-Adic Integers. In: Lindahl, K., Lindström, T., Rodino, L., Toft, J., Wahlberg, P. (eds) Analysis, Probability, Applications, and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-04459-6_22
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DOI: https://doi.org/10.1007/978-3-030-04459-6_22
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