UPM Institutional Repository

Cardinality of sets associated to certain degree seven polynomials


Lasaraiya, Suriana and Sapar, Siti Hasana and Mohamat Johari, Mohamat Aidil (2015) Cardinality of sets associated to certain degree seven polynomials. Malaysian Journal of Science, 34 (2). pp. 214-221. ISSN 0126-7906


Let f = f(x,y) be a function of two variables. Let q be an integer and let S(f;q) = ∑x mod qe 2πif(x)/q, where the sum is taken over a complete set of residue modulo q. The value of S(f;q) depends on the estimate of the cardinality |V| of the following set V={(x,y)mod q |fx, fy ≡ 0 mod q} where fx and fy are the partial derivative of f with respect to x and y. In this paper, we discuss the cardinality, |V| of the set of solutions for congruence equations of some special binary forms. Firstly we need to obtain the p-adic sizes of common zeros of the partial derivative polynomials by using Newton polyhedron technique. The polynomial that we consider is in the form of f(x, y) = ax7 + bx6y + cx5y2 + sx + ty + k.

Download File

PDF (Abstract)
Cardinality of sets associated to certain degree seven polynomials.pdf

Download (47kB) | Preview
Official URL or Download Paper: http://e-journal.um.edu.my/publish/MJS/925-1141

Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
Publisher: Faculty of Science, University of Malaya
Keywords: p-adic order; Newton polyhedron; Indicator diagram; Cardinality
Depositing User: Nabilah Mustapa
Date Deposited: 04 May 2017 04:43
Last Modified: 04 May 2017 04:43
URI: http://psasir.upm.edu.my/id/eprint/51969
Statistic Details: View Download Statistic

Actions (login required)

View Item View Item