On The Estimate to Solutions of Congruence Equations Associated with a Quartic form
The set of solutions to congruence equations modulo a prime power associated with the polynomial in Zp[x,y] is examined and its cardinality is estimated by employing the Newton polyhedral technique.The method involves reduction of the partial derivatives of f that is f" and fy into polynomi...
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1997
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| Online Access: | http://psasir.upm.edu.my/id/eprint/8621/1/FSAS_1997_6_A.pdf |
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my-upm-ir.86212012-05-08T07:14:49Z On The Estimate to Solutions of Congruence Equations Associated with a Quartic form 1997 Chan, Kait Loon The set of solutions to congruence equations modulo a prime power associated with the polynomial in Zp[x,y] is examined and its cardinality is estimated by employing the Newton polyhedral technique.The method involves reduction of the partial derivatives of f that is f" and fy into polynomials with single variable and finding 8 the determinant factor in the estimation. fx and fy are reduced to one-variable polynomials by employment of suitable parameters. The Newton polyhedrons associated with the polynomials so obtained are then considered and combination of their Indicator diagrams examined. There exist common zeros of the single- variable polynomials whose p-adic orders correspond to the intersection points in the combination of the Indicator diagrams associated with the respective Newton polyhedrons of the polynomials. The p-adic sizes of these zeros are then determined, and this leads to sizes of common zeros of the partial derivatives of f. This information is then used to arrive at the estimate of the cardinality above. Congruences and residues 1997 Thesis http://psasir.upm.edu.my/id/eprint/8621/ http://psasir.upm.edu.my/id/eprint/8621/1/FSAS_1997_6_A.pdf application/pdf en public masters Universiti Putra Malaysia Congruences and residues Faculty of Environmental Studies English |
| institution |
Universiti Putra Malaysia |
| collection |
PSAS Institutional Repository |
| language |
English English |
| topic |
Congruences and residues |
| spellingShingle |
Congruences and residues Chan, Kait Loon On The Estimate to Solutions of Congruence Equations Associated with a Quartic form |
| description |
The set of solutions to congruence equations modulo a prime power
associated with the polynomial
in Zp[x,y] is examined and its cardinality is estimated by employing the
Newton polyhedral technique.The method involves reduction of the partial derivatives of f that is f"
and fy into polynomials with single variable and finding 8 the determinant
factor in the estimation. fx and fy are reduced to one-variable polynomials by
employment of suitable parameters. The Newton polyhedrons associated with
the polynomials so obtained are then considered and combination of their
Indicator diagrams examined.
There exist common zeros of the single- variable polynomials whose
p-adic orders correspond to the intersection points in the combination of the
Indicator diagrams associated with the respective Newton polyhedrons of the
polynomials. The p-adic sizes of these zeros are then determined, and this
leads to sizes of common zeros of the partial derivatives of f. This information
is then used to arrive at the estimate of the cardinality above. |
| format |
Thesis |
| qualification_level |
Master's degree |
| author |
Chan, Kait Loon |
| author_facet |
Chan, Kait Loon |
| author_sort |
Chan, Kait Loon |
| title |
On The Estimate to Solutions of Congruence Equations Associated with a Quartic form |
| title_short |
On The Estimate to Solutions of Congruence Equations Associated with a Quartic form |
| title_full |
On The Estimate to Solutions of Congruence Equations Associated with a Quartic form |
| title_fullStr |
On The Estimate to Solutions of Congruence Equations Associated with a Quartic form |
| title_full_unstemmed |
On The Estimate to Solutions of Congruence Equations Associated with a Quartic form |
| title_sort |
on the estimate to solutions of congruence equations associated with a quartic form |
| granting_institution |
Universiti Putra Malaysia |
| granting_department |
Faculty of Environmental Studies |
| publishDate |
1997 |
| url |
http://psasir.upm.edu.my/id/eprint/8621/1/FSAS_1997_6_A.pdf |
| _version_ |
1747810841116278784 |