On the cardinality of twelfth degree polynomial
Let p be a prime and f (x, y) be a polynomial in Zp[x, y]. It is defined that the exponential sums associated with f modulo a prime pα is S(f:q)=∑e2πif(x)q for α>1, where f (x) is in Z[x] and the sum is taken over a complete set of residues x modulo positive integer q. Previous studies has shown...
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
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AIP Publishing
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57171/1/On%20the%20cardinality%20of%20twelfth%20degree%20polynomial.pdf |
| _version_ | 1796976637440425984 |
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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 p be a prime and f (x, y) be a polynomial in Zp[x, y]. It is defined that the exponential sums associated with f modulo a prime pα is S(f:q)=∑e2πif(x)q for α>1, where f (x) is in Z[x] and the sum is taken over a complete set of residues x modulo positive integer q. Previous studies has shown that estimation of S (f; pα) is depends on the cardinality of the set of solutions to congruence equation associated with the polynomial. In order to estimate the cardinality, we need to have the value of p-adic sizes of common zeros of partial derivative polynomials associated with polynomial. Hence, p-adic method and newton polyhedron technique will be applied to this approach. After that, indicator diagram will be constructed and analyzed. The cardinality will in turn be used to estimate the exponential sums of the polynomials. This paper concentrates on the cardinality of the set of solutions to congruence equation associated with polynomial in the form of f (x, y) = ax12 + bx11y + cx10y2 + sx + ty + k. |
| first_indexed | 2024-03-06T09:28:35Z |
| format | Conference or Workshop Item |
| id | upm.eprints-57171 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:28:35Z |
| publishDate | 2016 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | upm.eprints-571712017-09-08T05:30:27Z http://psasir.upm.edu.my/id/eprint/57171/ On the cardinality of twelfth degree polynomial Lasaraiya, Suriana Sapar, Siti Hasana Mohamat Johari, Mohamat Aidil Let p be a prime and f (x, y) be a polynomial in Zp[x, y]. It is defined that the exponential sums associated with f modulo a prime pα is S(f:q)=∑e2πif(x)q for α>1, where f (x) is in Z[x] and the sum is taken over a complete set of residues x modulo positive integer q. Previous studies has shown that estimation of S (f; pα) is depends on the cardinality of the set of solutions to congruence equation associated with the polynomial. In order to estimate the cardinality, we need to have the value of p-adic sizes of common zeros of partial derivative polynomials associated with polynomial. Hence, p-adic method and newton polyhedron technique will be applied to this approach. After that, indicator diagram will be constructed and analyzed. The cardinality will in turn be used to estimate the exponential sums of the polynomials. This paper concentrates on the cardinality of the set of solutions to congruence equation associated with polynomial in the form of f (x, y) = ax12 + bx11y + cx10y2 + sx + ty + k. AIP Publishing 2016 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57171/1/On%20the%20cardinality%20of%20twelfth%20degree%20polynomial.pdf Lasaraiya, Suriana and Sapar, Siti Hasana and Mohamat Johari, Mohamat Aidil (2016) On the cardinality of twelfth degree polynomial. In: 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016), 26-28 Jan. 2016, Kuala Lumpur, Malaysia. (pp. 1-9). http://aip.scitation.org/doi/abs/10.1063/1.4952488 10.1063/1.4952488 |
| spellingShingle | Lasaraiya, Suriana Sapar, Siti Hasana Mohamat Johari, Mohamat Aidil On the cardinality of twelfth degree polynomial |
| title | On the cardinality of twelfth degree polynomial |
| title_full | On the cardinality of twelfth degree polynomial |
| title_fullStr | On the cardinality of twelfth degree polynomial |
| title_full_unstemmed | On the cardinality of twelfth degree polynomial |
| title_short | On the cardinality of twelfth degree polynomial |
| title_sort | on the cardinality of twelfth degree polynomial |
| url | http://psasir.upm.edu.my/id/eprint/57171/1/On%20the%20cardinality%20of%20twelfth%20degree%20polynomial.pdf |
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