Sains Malaysiana 44(5)(2015): 765–769
The Number of
Solutions of Cubic Equations over Q3
(Beberapa Penyelesaian Persamaan Kubik ke atasQ3)
MANSOOR SABUROV* & MOHD ALI KHAMEINI AHMAD
Department
of Computational & Theoretical Sciences, Faculty of Sciences, International
Islamic University Malaysia, P.O. Box 25200 Kuantan, Pahang Darul Makmur, Malaysia
Diserahkan: 26 April 2014/Diterima:
18 November 2014
ABSTRACT
We provide the number of
solutions of a cubic equation in domains ,Q3 \ , Q3\ Q3 and Q3.
Keywords: Cubic equation; p–adic number; the number of solutions
ABSTRAK
Kami menyediakan beberapa penyelesaian persamaan kubik dalam domain , Q3 \ , Q3\ Q3 dan Q3.
Kata kunci: Beberapa penyelesaian; nombor p–adic; persamaan kubik
RUJUKAN
Apostol,
T.M. 1972. Introduction to Analytic Number Theory. New York: Springer-Verlag.
Beltrametti, E.
& Cassinelli, G. 1972. Quantum mechanics and p–adic numbers Found. Phys. 2: 1-7.
Borevich,
Z.I. & Shafarevich, I.R. 1966. Number Theory. New York: Acad. Press.
Cohen,
H. 2007. Number Theory, Volume I, II. New York: Springer.
Gouvea, F.Q. 1997. p–adic Numbers: An Introduction. Berlin:
Springer-Verlag.
Khrennikov, A.Y. 1991. p–adic quantum mechanics with p–adic valued
functions. J. Math. Phys. 32: 932.
Khrennikov, A.Y. 1994. p–Adic Valued
Distributions in Mathematical Physics. Netherlands: Springer.
Koblitz, N.
1984. p–adic numbers, p–adic Analysis, and Zeta Functions, 2nd
ed. New York: Springer.
Lang,
S. 1994. Algebraic Number Theory. New York:
Springer- Verlag.
Mukhamedov,
F., Omirov, B. & Saburov,
M. 2014. On cubic equations over p–adic field. International Journal of Number Theory 10(5): 1171-1190.
Mukhamedov,
F., Omirov, B., Saburov, M.
& Masutova, K. 2013. Solvability of cubic equations in p–adic integers, Siberian Mathematical Journal 54(3): 501-516.
Mukhamedov, F.
& Saburov, M. 2013. On
equation over Journal of Number Theory 133(1): 55-58.
Neukirch, J. 1999. Algebraic
Number Theory. Berlin, Heidelberg: Springer-Verlag.
Saburov, M.
& Ahmad, M.A. Kh. 2015. Solvability of cubic equations over Sains Malaysiana44(4): 635-641.
Saburov, M.
& Ahmad, M.A. Kh. 2014. Solvability criteria for cubic equations over AIP Conference Proceedings 1602:
792-797.
Schikhof, W.H. 1984. Ultrametric Calculus: An Introduction to p–adic Analysis. Cambridge:
Cambridge University Press.
Serre, J.P. 2003. On a theorem of Jordan. Bulletin of AMS. 40: 429-440.
Serre, J.P. 1979. Local Field. New
York: Springer-Verlag.
Sun, Z.H. 2007. Cubic
residues and binary quadratic forms. J. Numb. Theory 124(1):
62-104.
Sun,
Z.H. 1988. On the theory of cubic residues and non-residues. Acta Arith. 4: 291-335.
Volovich, I.V. 1987. p–adic strings. Class. Quantum
Gray.4(4): 83-87.
*Pengarang untuk surat-menyurat;
email: msaburov@gmail.com
|