Chan, Kait Loon (1997) On The Estimate to Solutions of Congruence Equations Associated with a Quartic form. Masters thesis, Universiti Putra Malaysia.
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.
|Item Type:||Thesis (Masters)|
|Subject:||Congruences and residues|
|Chairman Supervisor:||Professor Dr. Kamel Ariffin bin Mohd. Atan|
|Call Number:||FSAS 1997 6|
|Faculty or Institute:||Faculty of Environmental Studies|
|Deposited By:||Nurul Hayatie Hashim|
|Deposited On:||03 Dec 2010 17:05|
|Last Modified:||08 May 2012 15:14|
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