Exponential sums for some nth degree polynomial
Let f(x, y) be a polynomial in Zp[x, y] and p be a prime. For α > 1, the exponential sums associated with f(x, y) modulo a prime p α is defined as S(f ; p α) = epα (f(x, y)), where the sum is taken over a complete set of residues modulo p α. It has been shown that the exponential sums is de...
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my-upm-ir.669592019-02-13T00:56:05Z Exponential sums for some nth degree polynomial 2016-10 Lasaraiya, Suriana Let f(x, y) be a polynomial in Zp[x, y] and p be a prime. For α > 1, the exponential sums associated with f(x, y) modulo a prime p α is defined as S(f ; p α) = epα (f(x, y)), where the sum is taken over a complete set of residues modulo p α. It has been shown that the exponential sums is depends on the cardinality of the set of solutions to the congruence equation associated with the polynomial f(x, y). The objective of this research is to find an estimation of the exponential sums for some n th degree polynomial at any point (x−x0, y−y0). There are two conditions being considered, that is for ordpb 2 6= ordpac and ordpb 2 = ordpac. The p-adic methods and Newton polyhedron technique is used to estimate the p-adic sizes of common zeros of partial derivative polynomials associated with n th degree polynomial, where n ≥ 3. Then, construct the combination of indicator diagram associated with some n th degree polynomial. The indicator diagram is then examined and analyzed. The information of p-adic sizes of common zeros that obtained is applied to estimate the cardinality of the set V(fx, fy; p α). The results of the cardinality is then used to estimate the estimation of exponential sums associated to n th degree polynomial, where n ≥ 3. Polynomials Algebra, Universal 2016-10 Thesis http://psasir.upm.edu.my/id/eprint/66959/ http://psasir.upm.edu.my/id/eprint/66959/1/IPM%202016%2019%20IR.pdf text en public masters Universiti Putra Malaysia Polynomials Algebra, Universal |
| institution |
Universiti Putra Malaysia |
| collection |
PSAS Institutional Repository |
| language |
English |
| topic |
Polynomials Polynomials |
| spellingShingle |
Polynomials Polynomials Lasaraiya, Suriana Exponential sums for some nth degree polynomial |
| description |
Let f(x, y) be a polynomial in Zp[x, y] and p be a prime. For α > 1, the exponential
sums associated with f(x, y) modulo a prime p
α is defined as S(f ; p
α) =
epα (f(x, y)), where the sum is taken over a complete set of residues modulo p
α. It
has been shown that the exponential sums is depends on the cardinality of the set
of solutions to the congruence equation associated with the polynomial f(x, y). The
objective of this research is to find an estimation of the exponential sums for some
n
th degree polynomial at any point (x−x0, y−y0). There are two conditions being
considered, that is for ordpb
2 6= ordpac and ordpb
2 = ordpac.
The p-adic methods and Newton polyhedron technique is used to estimate the p-adic
sizes of common zeros of partial derivative polynomials associated with n
th degree
polynomial, where n ≥ 3. Then, construct the combination of indicator diagram associated
with some n
th degree polynomial. The indicator diagram is then examined
and analyzed.
The information of p-adic sizes of common zeros that obtained is applied to estimate
the cardinality of the set V(fx, fy; p
α). The results of the cardinality is then used to
estimate the estimation of exponential sums associated to n
th degree polynomial,
where n ≥ 3. |
| format |
Thesis |
| qualification_level |
Master's degree |
| author |
Lasaraiya, Suriana |
| author_facet |
Lasaraiya, Suriana |
| author_sort |
Lasaraiya, Suriana |
| title |
Exponential sums for some nth degree polynomial |
| title_short |
Exponential sums for some nth degree polynomial |
| title_full |
Exponential sums for some nth degree polynomial |
| title_fullStr |
Exponential sums for some nth degree polynomial |
| title_full_unstemmed |
Exponential sums for some nth degree polynomial |
| title_sort |
exponential sums for some nth degree polynomial |
| granting_institution |
Universiti Putra Malaysia |
| publishDate |
2016 |
| url |
http://psasir.upm.edu.my/id/eprint/66959/1/IPM%202016%2019%20IR.pdf |
| _version_ |
1747812430415659008 |