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Exponential sums for eighth degree polynomial


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. 115-138. ISSN 1823-8343; ESSN: 2289-750X


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 p-adic 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: P-adic 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
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