Exponential sums for eighth degree polynomial
Let p > 7 be a prime, the exponential sums of any polynomial f(x, y) is given by S(f; p α ) = ∑x,y mod p e 2πif(x,y)/ pα, where the sum is taken over a complete set of residue modulo p. Firstly, Newton Polyhedron technique was used to determine the estimation for the p-adic sizes of common zeros...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Institute for Mathematical Research, Universiti Putra Malaysia
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/38340/1/7.%20Siti%20Hasana%20Sapar.pdf |
| _version_ | 1825949207357292544 |
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| author | Low, Chee Wai Sapar, Siti Hasana Mohamat Johari, Mohamat Aidil |
| author_facet | Low, Chee Wai Sapar, Siti Hasana Mohamat Johari, Mohamat Aidil |
| author_sort | Low, Chee Wai |
| collection | UPM |
| description | Let p > 7 be a prime, the exponential sums of any polynomial f(x, y) is given by S(f; p α ) = ∑x,y mod p e 2πif(x,y)/ pα, where the sum is taken over a complete set of residue modulo p. Firstly, Newton Polyhedron technique was used to determine the estimation for the p-adic sizes of common zeros of the partial derivative polynomials fx, fy which derive from f(x, y). We continue by estimating the cardinality N(g, h; p α ) as well as the exponential sums of polynomial f(x, y). Throught out this paper, we consider the polynomial of eighth degree with two variables in the form f(x, y) = ax8 +bx7 y+cx6 y 2 +dx5 y 3 +ex4 y 4 +kx3 y 5 +mx2 y 6 + nxy7 + uy8 + rx + sy + t. |
| first_indexed | 2024-03-06T08:41:01Z |
| format | Article |
| id | upm.eprints-38340 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:41:01Z |
| publishDate | 2020 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| record_format | dspace |
| spelling | upm.eprints-383402020-05-04T16:19:15Z http://psasir.upm.edu.my/id/eprint/38340/ Exponential sums for eighth degree polynomial Low, Chee Wai Sapar, Siti Hasana Mohamat Johari, Mohamat Aidil Let p > 7 be a prime, the exponential sums of any polynomial f(x, y) is given by S(f; p α ) = ∑x,y mod p e 2πif(x,y)/ pα, where the sum is taken over a complete set of residue modulo p. Firstly, Newton Polyhedron technique was used to determine the estimation for the p-adic sizes of common zeros of the partial derivative polynomials fx, fy which derive from f(x, y). We continue by estimating the cardinality N(g, h; p α ) as well as the exponential sums of polynomial f(x, y). Throught out this paper, we consider the polynomial of eighth degree with two variables in the form f(x, y) = ax8 +bx7 y+cx6 y 2 +dx5 y 3 +ex4 y 4 +kx3 y 5 +mx2 y 6 + nxy7 + uy8 + rx + sy + t. Institute for Mathematical Research, Universiti Putra Malaysia 2020 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/38340/1/7.%20Siti%20Hasana%20Sapar.pdf Low, Chee Wai and Sapar, Siti Hasana and Mohamat Johari, Mohamat Aidil (2020) Exponential sums for eighth degree polynomial. Malaysian Journal of Mathematical Sciences, 14 (1). pp. 115-138. ISSN 1823-8343; ESSN: 2289-750X http://einspem.upm.edu.my/journal/fullpaper/vol14no1jan/7.%20Siti%20Hasana%20Sapar.pdf |
| spellingShingle | Low, Chee Wai Sapar, Siti Hasana Mohamat Johari, Mohamat Aidil Exponential sums for eighth degree polynomial |
| title | Exponential sums for eighth degree polynomial |
| title_full | Exponential sums for eighth degree polynomial |
| title_fullStr | Exponential sums for eighth degree polynomial |
| title_full_unstemmed | Exponential sums for eighth degree polynomial |
| title_short | Exponential sums for eighth degree polynomial |
| title_sort | exponential sums for eighth degree polynomial |
| url | http://psasir.upm.edu.my/id/eprint/38340/1/7.%20Siti%20Hasana%20Sapar.pdf |
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