A method of estimating the p-adic sizes polynomials
The exponential sum associated with f is defined as S (f; q) = ∑x mod q , where the sum is taken over a complete set of residues modulo q. The value of S (f; q) depends on the estimate of cardinality in the set V = {x mod q|fx 0 mod q} where fx is the partial derivatives of f with respect to x. In...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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North Atlantic Univeristy Union
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/36181/ http://psasir.upm.edu.my/id/eprint/36181/1/A%20method%20of%20estimating%20the%20p.pdf |
| _version_ | 1848848260698996736 |
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| author | Sapar, Siti Hasana Aminudin, Siti Syaheera Mohd Atan, Kamel Ariffin |
| author_facet | Sapar, Siti Hasana Aminudin, Siti Syaheera Mohd Atan, Kamel Ariffin |
| author_sort | Sapar, Siti Hasana |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The exponential sum associated with f is defined as S (f; q) = ∑x mod q , where the sum is taken over a complete set of residues modulo q. The value of S (f; q) depends on the estimate of cardinality in the set V = {x mod q|fx 0 mod q} where fx is the partial derivatives of f with respect to x. In order to determine the cardinality, the p-adic sizes of common zeros of the partial derivative polynomials need to be obtained. This paper will give an estimation of the p-adic sizes of common zeros of partial derivative polynomials of degree eight in p by using Newton polyhedron technique.
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| first_indexed | 2025-11-15T09:31:41Z |
| format | Article |
| id | upm-36181 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:31:41Z |
| publishDate | 2014 |
| publisher | North Atlantic Univeristy Union |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-361812016-01-28T01:31:00Z http://psasir.upm.edu.my/id/eprint/36181/ A method of estimating the p-adic sizes polynomials Sapar, Siti Hasana Aminudin, Siti Syaheera Mohd Atan, Kamel Ariffin The exponential sum associated with f is defined as S (f; q) = ∑x mod q , where the sum is taken over a complete set of residues modulo q. The value of S (f; q) depends on the estimate of cardinality in the set V = {x mod q|fx 0 mod q} where fx is the partial derivatives of f with respect to x. In order to determine the cardinality, the p-adic sizes of common zeros of the partial derivative polynomials need to be obtained. This paper will give an estimation of the p-adic sizes of common zeros of partial derivative polynomials of degree eight in p by using Newton polyhedron technique. North Atlantic Univeristy Union 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/36181/1/A%20method%20of%20estimating%20the%20p.pdf Sapar, Siti Hasana and Aminudin, Siti Syaheera and Mohd Atan, Kamel Ariffin (2014) A method of estimating the p-adic sizes polynomials. International Journal of Pure Mathematics, 1. pp. 22-29. ISSN 2313-0571 http://www.naun.org/cms.action?id=7635 |
| spellingShingle | Sapar, Siti Hasana Aminudin, Siti Syaheera Mohd Atan, Kamel Ariffin A method of estimating the p-adic sizes polynomials |
| title | A method of estimating the p-adic sizes polynomials |
| title_full | A method of estimating the p-adic sizes polynomials |
| title_fullStr | A method of estimating the p-adic sizes polynomials |
| title_full_unstemmed | A method of estimating the p-adic sizes polynomials |
| title_short | A method of estimating the p-adic sizes polynomials |
| title_sort | method of estimating the p-adic sizes polynomials |
| url | http://psasir.upm.edu.my/id/eprint/36181/ http://psasir.upm.edu.my/id/eprint/36181/ http://psasir.upm.edu.my/id/eprint/36181/1/A%20method%20of%20estimating%20the%20p.pdf |