Sains Malaysiana 40(8)(2011): 921–926
Estimation of p-adic sizes of Common Zeros of
Partial Derivatives Associated with a Cubic Form
(Penganggaran Saiz p-Adic
Pensifar Sepunya Polinomial-polinomial Terbitan Separa disekutukan dengan
Bentuk Kubik)
H.K. Yap*, K.A. Mohd Atan
& S.H. Sapar
Institute
for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang
Selangor,
Malaysia
Diserahkan: 13
November 2009 / Diterima: 17 Januari 2011
ABSTRACT
In this paper we determined
the estimate of p-adic sizes of common zeros of partial derivative polynomials
associated with a cubic form whose indicator diagrams have one overlapping
segment by using Newton polyhedron technique. We showed that the p-adic
sizes of such common zeros can be found explicitly on the overlapping segment
of the indicator diagrams associated with the polynomials.
Keywords: Indicator diagram;
newton polyhedron; overlapping segment; p-adic sizes
ABSTRAK
Dalam makalah ini kami menganggarkan saiz p-adic pensifar
sepunya polinomial-polinomial terbitan separa disekutukan dengan bentuk kubik
dan gambar rajah penunjuknya mempunyai satu tembereng bertindih dengan
menggunakan teknik polihedron Newton. Kami menunjukkan bahawa saiz p-adic
bagi pensifar sepunya tersebut boleh didapati secara eksplisit pada tembereng
bertindih dalam gambar rajah penunjuk disekutukan dengan polinomial terbabit.
Kata kunci:
Gambar rajah penunjuk; polihedron Newton; saiz p-adic; tembereng bertindih
RUJUKAN
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*Pengarang
untuk surat-menyurat; email: yaphongkeat@inspem.upm.edu.my
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