Cardinality of sets associated to certain degree seven polynomials
Let f = f(x,y) be a function of two variables. Let q be an integer and let S(f;q) = ∑x mod qe 2πif(x)/q, where the sum is taken over a complete set of residue modulo q. The value of S(f;q) depends on the estimate of the cardinality |V| of the following set V={(x,y)mod q |fx, fy ≡ 0 mod q} where fx a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Faculty of Science, University of Malaya
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/51969/1/Cardinality%20of%20sets%20associated%20to%20certain%20degree%20seven%20polynomials.pdf |
| _version_ | 1796975649834926080 |
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| author | Lasaraiya, Suriana Sapar, Siti Hasana Mohamat Johari, Mohamat Aidil |
| author_facet | Lasaraiya, Suriana Sapar, Siti Hasana Mohamat Johari, Mohamat Aidil |
| author_sort | Lasaraiya, Suriana |
| collection | UPM |
| description | Let f = f(x,y) be a function of two variables. Let q be an integer and let S(f;q) = ∑x mod qe 2πif(x)/q, where the sum is taken over a complete set of residue modulo q. The value of S(f;q) depends on the estimate of the cardinality |V| of the following set V={(x,y)mod q |fx, fy ≡ 0 mod q} where fx and fy are the partial derivative of f with respect to x and y. In this paper, we discuss the cardinality, |V| of the set of solutions for congruence equations of some special binary forms. Firstly we need to obtain the p-adic sizes of common zeros of the partial derivative polynomials by using Newton polyhedron technique. The polynomial that we consider is in the form of f(x, y) = ax7 + bx6y + cx5y2 + sx + ty + k. |
| first_indexed | 2024-03-06T09:14:31Z |
| format | Article |
| id | upm.eprints-51969 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:14:31Z |
| publishDate | 2015 |
| publisher | Faculty of Science, University of Malaya |
| record_format | dspace |
| spelling | upm.eprints-519692017-05-04T04:43:37Z http://psasir.upm.edu.my/id/eprint/51969/ Cardinality of sets associated to certain degree seven polynomials Lasaraiya, Suriana Sapar, Siti Hasana Mohamat Johari, Mohamat Aidil Let f = f(x,y) be a function of two variables. Let q be an integer and let S(f;q) = ∑x mod qe 2πif(x)/q, where the sum is taken over a complete set of residue modulo q. The value of S(f;q) depends on the estimate of the cardinality |V| of the following set V={(x,y)mod q |fx, fy ≡ 0 mod q} where fx and fy are the partial derivative of f with respect to x and y. In this paper, we discuss the cardinality, |V| of the set of solutions for congruence equations of some special binary forms. Firstly we need to obtain the p-adic sizes of common zeros of the partial derivative polynomials by using Newton polyhedron technique. The polynomial that we consider is in the form of f(x, y) = ax7 + bx6y + cx5y2 + sx + ty + k. Faculty of Science, University of Malaya 2015 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/51969/1/Cardinality%20of%20sets%20associated%20to%20certain%20degree%20seven%20polynomials.pdf Lasaraiya, Suriana and Sapar, Siti Hasana and Mohamat Johari, Mohamat Aidil (2015) Cardinality of sets associated to certain degree seven polynomials. Malaysian Journal of Science, 34 (2). pp. 214-221. ISSN 0126-7906 http://e-journal.um.edu.my/publish/MJS/925-1141 |
| spellingShingle | Lasaraiya, Suriana Sapar, Siti Hasana Mohamat Johari, Mohamat Aidil Cardinality of sets associated to certain degree seven polynomials |
| title | Cardinality of sets associated to certain degree seven polynomials |
| title_full | Cardinality of sets associated to certain degree seven polynomials |
| title_fullStr | Cardinality of sets associated to certain degree seven polynomials |
| title_full_unstemmed | Cardinality of sets associated to certain degree seven polynomials |
| title_short | Cardinality of sets associated to certain degree seven polynomials |
| title_sort | cardinality of sets associated to certain degree seven polynomials |
| url | http://psasir.upm.edu.my/id/eprint/51969/1/Cardinality%20of%20sets%20associated%20to%20certain%20degree%20seven%20polynomials.pdf |
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