Penganggaran saiz p-adic pensifar sepunya terbitan separa polinomial berdarjah enam
It is known that the value of the exponential sum S(f;pα) depends on the estimate of the cardinality [V], the number of elements contained in the set V = {x mod pα/fx ≡ 0 mod pα} where fx is the partial derivatives of f with respect to x. The cardinality of V in turn depends on the p-adic sizes of c...
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2007
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| Online Access: | http://psasir.upm.edu.my/id/eprint/28170/1/Penganggaran%20saiz%20p-adic%20pensifar%20sepunya%20terbitan%20separa%20polinomial%20berdarjah%20enam.pdf |
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| author | Sapar, Siti Hasana Mohd Atan, Kamel Ariffin |
| author_facet | Sapar, Siti Hasana Mohd Atan, Kamel Ariffin |
| author_sort | Sapar, Siti Hasana |
| collection | UPM |
| description | It is known that the value of the exponential sum S(f;pα) depends on the estimate of the cardinality [V], the number of elements contained in the set V = {x mod pα/fx ≡ 0 mod pα} where fx is the partial derivatives of f with respect to x. The cardinality of V in turn depends on the p-adic sizes of common zeros of the partial derivatives fx. This paper presents a methods of determining the p-adic of the components of (ξη) a common root of partial derivative polynomials of f(x,y) in Zp[x,y] of degree six based on the p-adic Newton polyhedron technique associated with the polynomial. The degree six polynomial is of the form f(x,y) = ax6 + bx5y + cx4y2 + dx3y3 + ex2y4 + mxy5 + ny6 + sx + ty + k. The estimate obtained is in terms of the p-adic sizes of the coefficients of the dominant terms in f. |
| first_indexed | 2024-03-06T08:10:34Z |
| format | Article |
| id | upm.eprints-28170 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:10:34Z |
| publishDate | 2007 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| record_format | dspace |
| spelling | upm.eprints-281702016-02-02T05:35:21Z http://psasir.upm.edu.my/id/eprint/28170/ Penganggaran saiz p-adic pensifar sepunya terbitan separa polinomial berdarjah enam Sapar, Siti Hasana Mohd Atan, Kamel Ariffin It is known that the value of the exponential sum S(f;pα) depends on the estimate of the cardinality [V], the number of elements contained in the set V = {x mod pα/fx ≡ 0 mod pα} where fx is the partial derivatives of f with respect to x. The cardinality of V in turn depends on the p-adic sizes of common zeros of the partial derivatives fx. This paper presents a methods of determining the p-adic of the components of (ξη) a common root of partial derivative polynomials of f(x,y) in Zp[x,y] of degree six based on the p-adic Newton polyhedron technique associated with the polynomial. The degree six polynomial is of the form f(x,y) = ax6 + bx5y + cx4y2 + dx3y3 + ex2y4 + mxy5 + ny6 + sx + ty + k. The estimate obtained is in terms of the p-adic sizes of the coefficients of the dominant terms in f. Penerbit Universiti Kebangsaan Malaysia 2007 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/28170/1/Penganggaran%20saiz%20p-adic%20pensifar%20sepunya%20terbitan%20separa%20polinomial%20berdarjah%20enam.pdf Sapar, Siti Hasana and Mohd Atan, Kamel Ariffin (2007) Penganggaran saiz p-adic pensifar sepunya terbitan separa polinomial berdarjah enam. Sains Malaysiana, 36 (1). pp. 77-82. ISSN 0126-6039 http://www.ukm.my/jsm/english_journals/vol36num1_2007/vol36num1_07page77-82.html |
| spellingShingle | Sapar, Siti Hasana Mohd Atan, Kamel Ariffin Penganggaran saiz p-adic pensifar sepunya terbitan separa polinomial berdarjah enam |
| title | Penganggaran saiz p-adic pensifar sepunya terbitan separa polinomial berdarjah enam |
| title_full | Penganggaran saiz p-adic pensifar sepunya terbitan separa polinomial berdarjah enam |
| title_fullStr | Penganggaran saiz p-adic pensifar sepunya terbitan separa polinomial berdarjah enam |
| title_full_unstemmed | Penganggaran saiz p-adic pensifar sepunya terbitan separa polinomial berdarjah enam |
| title_short | Penganggaran saiz p-adic pensifar sepunya terbitan separa polinomial berdarjah enam |
| title_sort | penganggaran saiz p adic pensifar sepunya terbitan separa polinomial berdarjah enam |
| url | http://psasir.upm.edu.my/id/eprint/28170/1/Penganggaran%20saiz%20p-adic%20pensifar%20sepunya%20terbitan%20separa%20polinomial%20berdarjah%20enam.pdf |
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