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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| Main Author: | |
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| Format: | Thesis |
| Language: | English English |
| Published: |
1997
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/8621/1/FSAS_1997_6_A.pdf |
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| Summary: | 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. |
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