On The Estimate to Solutions of Congruence Equations Associated with a Quartic form

Chan, Kait Loon (1997) On The Estimate to Solutions of Congruence Equations Associated with a Quartic form. Masters thesis, Universiti Pertanian Malaysia.

[img] PDF
1306Kb

Abstract

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
ID Code:8621
Deposited By: Nurul Hayatie Hashim
Deposited On:03 Dec 2010 09:05
Last Modified:08 May 2012 07:14

Repository Staff Only: item control page

Document Download Statistics

This item has been downloaded for since 03 Dec 2010 09:05.

View statistics for "On The Estimate to Solutions of Congruence Equations Associated with a Quartic form"


Universiti Putra Malaysia Institutional Repository

Universiti Putra Malaysia Institutional Repository is an on-line digital archive that serves as a central collection and storage of scientific information and research at the Universiti Putra Malaysia.

Currently, the collections deposited in the IR consists of Master and PhD theses, Master and PhD Project Report, Journal Articles, Journal Bulletins, Conference Papers, UPM News, Newspaper Cuttings, Patents and Inaugural Lectures.

As the policy of the university does not permit users to view thesis in full text, access is only given to the first 24 pages only.