A Method of Estimating the p-adic Sizes of Common Zeros of Partial Derivative Polynomials Associated with a Seventh Degree Form

Sapar, Siti Hasana and Mohd Atan, Kamel Ariffin and Mohd Said, Mohamad Rushdan (2007) A Method of Estimating the p-adic Sizes of Common Zeros of Partial Derivative Polynomials Associated with a Seventh Degree Form. Pertanika Journal of Science & Technology, 15 (1). pp. 61-76. ISSN 0128-7680

Full text not available from this repository.

Abstract

Let x = (x1, x2,...,xn) be a vector in a space Zn where Z is the ring of integers and let q be a positive integer, f a polynomial in x with coefficients in Z. The exponential sum associated with f is defined as S(f;q) = Σ exp(2πif(x)/q) where the sum is taken over a complete set of residues modulo q. The value of S(f;q) has been shown to depend on the estimate of the cardinality V , the number of elements contained in the set V={Xmodq fx≡ 0 mod q} where fx is the partial derivatives off with respect to x. To determine the cardinality of V, the information on the p-adic sizes of common zeros of the partial derivatives polynomials need to be obtained. This paper discusses a method of determining the p-adic sizes of the components of (ξ,η), a common root of partial derivatives polynomial of f(x,y) in of degree n, where n is odd based on the p-adic Newton polyhedron technique associated with the polynomial. The polynomial of degree n is of the form f(x, y) = axn + bxn-1 y + cxn-2 y2 + sx + ty + k.

Item Type:Article
Keyword:Partial derivative polynomials, seventh degree form, Newton polyhedron technique
Faculty or Institute:Faculty of Science
Publisher:Universiti Putra Malaysia Press
ID Code:11966
Deposited By: Najwani Amir Sariffudin
Deposited On:21 Apr 2011 08:32
Last Modified:21 Apr 2011 08:32

Repository Staff Only: item control page


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.