A method of estimating the p-adic sizes of common zeros of partial derivative polynomials associated with a quintic form
It is known that the value of the exponential sum can be derived from the estimate of the cardinality |V|, the number of elements contained in the set where is the partial derivatives of with respect to . The cardinality of V in turn can be derived from the p-adic sizes of common zeros of the partia...
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| Format: | Article |
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World Scientific Publishing
2009
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| _version_ | 1796968285449748480 |
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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 can be derived from the estimate of the cardinality |V|, the number of elements contained in the set where is the partial derivatives of with respect to . The cardinality of V in turn can be derived from the p-adic sizes of common zeros of the partial derivatives . This paper presents a method of determining the p-adic sizes of the components of (ξ,η) a common root of partial derivative polynomials of f(x,y) in Zp[x,y] of degree five based on the p-adic Newton polyhedron technique associated with the polynomial. The degree five polynomial is of the form f(x,y) = ax5 + bx4y + cx3y2 + 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 | 2024-03-06T07:26:13Z |
| format | Article |
| id | upm.eprints-12721 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-03-06T07:26:13Z |
| publishDate | 2009 |
| publisher | World Scientific Publishing |
| record_format | dspace |
| spelling | upm.eprints-127212015-06-22T01:11:18Z http://psasir.upm.edu.my/id/eprint/12721/ A method of estimating the p-adic sizes of common zeros of partial derivative polynomials associated with a quintic form Sapar, Siti Hasana Mohd Atan, Kamel Ariffin It is known that the value of the exponential sum can be derived from the estimate of the cardinality |V|, the number of elements contained in the set where is the partial derivatives of with respect to . The cardinality of V in turn can be derived from the p-adic sizes of common zeros of the partial derivatives . This paper presents a method of determining the p-adic sizes of the components of (ξ,η) a common root of partial derivative polynomials of f(x,y) in Zp[x,y] of degree five based on the p-adic Newton polyhedron technique associated with the polynomial. The degree five polynomial is of the form f(x,y) = ax5 + bx4y + cx3y2 + sx + ty + k. The estimate obtained is in terms of the p-adic sizes of the coefficients of the dominant terms in f. World Scientific Publishing 2009-05 Article PeerReviewed Sapar, Siti Hasana and Mohd Atan, Kamel Ariffin (2009) A method of estimating the p-adic sizes of common zeros of partial derivative polynomials associated with a quintic form. International Journal of Number Theory, 5 (3). pp. 541-554. ISSN 1793-0421; ESSN: 1793-7310 http://www.worldscientific.com/doi/abs/10.1142/S1793042109002249 10.1142/S1793042109002249 |
| spellingShingle | Sapar, Siti Hasana Mohd Atan, Kamel Ariffin A method of estimating the p-adic sizes of common zeros of partial derivative polynomials associated with a quintic form |
| title | A method of estimating the p-adic sizes of common zeros of partial derivative polynomials associated with a quintic form |
| title_full | A method of estimating the p-adic sizes of common zeros of partial derivative polynomials associated with a quintic form |
| title_fullStr | A method of estimating the p-adic sizes of common zeros of partial derivative polynomials associated with a quintic form |
| title_full_unstemmed | A method of estimating the p-adic sizes of common zeros of partial derivative polynomials associated with a quintic form |
| title_short | A method of estimating the p-adic sizes of common zeros of partial derivative polynomials associated with a quintic form |
| title_sort | method of estimating the p adic sizes of common zeros of partial derivative polynomials associated with a quintic form |
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