Citation
Low, Chee Wai and Sapar, Siti Hasana and Mohamat Johari, Mohamat Aidil
(2020)
Exponential sums for eighth degree polynomial.
Malaysian Journal of Mathematical Sciences, 14 (1).
pp. 115138.
ISSN 18238343; ESSN: 2289750X
Abstract
Let p > 7 be a prime, the exponential sums of any polynomial f(x, y) is given by S(f; p α ) = ∑x,y mod p e 2πif(x,y)/ pα, where the sum is taken over a complete set of residue modulo p. Firstly, Newton Polyhedron technique was used to determine the estimation for the padic sizes of common zeros of the partial derivative polynomials fx, fy which derive from f(x, y). We continue by estimating the cardinality N(g, h; p α ) as well as the exponential sums of polynomial f(x, y). Throught out this paper, we consider the polynomial of eighth degree with two variables in the form f(x, y) = ax8 +bx7 y+cx6 y 2 +dx5 y 3 +ex4 y 4 +kx3 y 5 +mx2 y 6 + nxy7 + uy8 + rx + sy + t.
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Additional Metadata
Item Type:  Article 

Divisions:  Faculty of Science Institute for Mathematical Research 
Publisher:  Institute for Mathematical Research, Universiti Putra Malaysia 
Keywords:  Padic sizes; Newton polyhedron; Indicator diagram; Cardinality; Exponential sums 
Depositing User:  Nabilah Mustapa 
Date Deposited:  04 May 2020 16:19 
Last Modified:  04 May 2020 16:19 
URI:  http://psasir.upm.edu.my/id/eprint/38340 
Statistic Details:  View Download Statistic 
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