On the cardinality of the set of solutions to congruence equation associated with polynomial of degree eleven
Let p be a prime and f(x, y) be a polynomial in Zp[x, y]. For α > 1, the exponential sums associated with f modulo a prime pα is defined as S(f;q)= ∑e2πif(x)/q. It has been shown that the estimation of S(f; pα)depends on the cardinality of the set of solutions to the congruence equation associate...
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| Format: | Conference or Workshop Item |
| Language: | English |
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AIP Publishing
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57664/ http://psasir.upm.edu.my/id/eprint/57664/1/On%20the%20cardinality%20of%20the%20set%20of%20solutions%20to%20congruence%20equation%20associated%20with%20polynomial%20of%20degree%20eleven.pdf |
| _version_ | 1848853429375467520 |
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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 |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Let p be a prime and f(x, y) be a polynomial in Zp[x, y]. For α > 1, the exponential sums associated with f modulo a prime pα is defined as S(f;q)= ∑e2πif(x)/q. It has been shown that the estimation of S(f; pα)depends on the cardinality of the set of solutions to the congruence equation associated with the polynomial. In order to estimate the p-adic sizes of common zeros of partial derivative polynomials associated with certain class of polynomial of degree eleven, the Newton polyhedron technique will be used. Then, the indicator diagram is constructed and analyzed. Hence, the estimation of the cardinality of the set of the solutions is determined. |
| first_indexed | 2025-11-15T10:53:50Z |
| format | Conference or Workshop Item |
| id | upm-57664 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:53:50Z |
| publishDate | 2015 |
| publisher | AIP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-576642017-10-25T01:35:05Z http://psasir.upm.edu.my/id/eprint/57664/ On the cardinality of the set of solutions to congruence equation associated with polynomial of degree eleven 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]. For α > 1, the exponential sums associated with f modulo a prime pα is defined as S(f;q)= ∑e2πif(x)/q. It has been shown that the estimation of S(f; pα)depends on the cardinality of the set of solutions to the congruence equation associated with the polynomial. In order to estimate the p-adic sizes of common zeros of partial derivative polynomials associated with certain class of polynomial of degree eleven, the Newton polyhedron technique will be used. Then, the indicator diagram is constructed and analyzed. Hence, the estimation of the cardinality of the set of the solutions is determined. AIP Publishing 2015 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57664/1/On%20the%20cardinality%20of%20the%20set%20of%20solutions%20to%20congruence%20equation%20associated%20with%20polynomial%20of%20degree%20eleven.pdf Lasaraiya, Suriana and Sapar, Siti Hasana and Mohamat Johari, Mohamat Aidil (2015) On the cardinality of the set of solutions to congruence equation associated with polynomial of degree eleven. In: 23rd Malaysian National Symposium of Mathematical Sciences (SKSM23), 24-26 Nov. 2015, Johor Bahru, Malaysia. (pp. 1-10). 10.1063/1.4954603 |
| spellingShingle | Lasaraiya, Suriana Sapar, Siti Hasana Mohamat Johari, Mohamat Aidil On the cardinality of the set of solutions to congruence equation associated with polynomial of degree eleven |
| title | On the cardinality of the set of solutions to congruence equation associated with polynomial of degree eleven |
| title_full | On the cardinality of the set of solutions to congruence equation associated with polynomial of degree eleven |
| title_fullStr | On the cardinality of the set of solutions to congruence equation associated with polynomial of degree eleven |
| title_full_unstemmed | On the cardinality of the set of solutions to congruence equation associated with polynomial of degree eleven |
| title_short | On the cardinality of the set of solutions to congruence equation associated with polynomial of degree eleven |
| title_sort | on the cardinality of the set of solutions to congruence equation associated with polynomial of degree eleven |
| url | http://psasir.upm.edu.my/id/eprint/57664/ http://psasir.upm.edu.my/id/eprint/57664/ http://psasir.upm.edu.my/id/eprint/57664/1/On%20the%20cardinality%20of%20the%20set%20of%20solutions%20to%20congruence%20equation%20associated%20with%20polynomial%20of%20degree%20eleven.pdf |