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Applicable Analysis and Discrete Mathematics
2010, vol. 4, iss. 1, pp. 32-44
article language: English
unclassified
doi:10.2298/AADM1000009M
Hensel codes of square roots of p-adic numbers
Tahar Zerzaihia, Mohamed Keciesa, Knapp Michael P.b
aLaboratoire de mathématiques pures et appliquées, BP Ouled Aissa, Université de Jijel, Algeria
bDepartment of Mathematical Sciences, Loyola University Maryland, Baltimore, USA

e-mail: zerzaihi@yahoo.fr, kecmohamed@yahoo.fr, mpknapp@lo

Abstract

In this work we are concerned with the calculation of the Hensel codes of square roots of p-adic numbers, using the fixed point method and this through the calculation of the approached solution of f(x)=x2-a=0 in Qp. We also determine the speed of convergence and the number of iterations.

Keywords

P-adic number; square root; Hensel code; fixed point; speed of convergence

References

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Knapp, M., Xenophotos, C. (2004) Numerical analysis meets number theory: Using rootfinding methods to calculate inverses mod pn. Baltimore: Mathematical Sciences Department, Loyola College, Jun. 17

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Koc, Ç.K. (2002) A tutorial on p-adic arithmetic: Electrical & computer engineering. Oregon: Oregon State University Corvallis, Technical report, april