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

Received: 13 November 2009 / Accepted: 17 January 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

REFERENCES

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*Corresponding author; email: yaphongkeat@inspem.upm.edu.my