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- W1991223639 abstract "Let x¯ = (x1,x2,...,xn) be a vector in Zn with Z ring of integers and q be a positive integer, f a polynomial in x with coefficient in Z. The exponential sum associated with f is defined as S(f;q) = ∑ xmodqe2πif(x)q, where the sum is taken over a complete set of residues modulo q. The value of S (f; q) depends on the estimate of cardinality |V|, the number of elements contained in the set V = {x¯modq|f¯x¯≡0¯modq} where f¯x¯ is the partial derivatives of f with respect to x. To determine the cardinality of V, the p-adic sizes of common zeros of the partial derivative polynomials need to be obtained. In this paper, we estimate the p-adic sizes of common zeros of partial derivative polynomials of f(x,y) in Zp[x,y] with a sixth degree form by using Newton polyhedron technique. The polynomial is of the form f(x,y) = ax6+bx5y+cx4y2+sx+ty+k." @default.
- W1991223639 created "2016-06-24" @default.
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- W1991223639 date "2014-01-01" @default.
- W1991223639 modified "2023-10-11" @default.
- W1991223639 title "An estimation of the p-adic sizes of common zeros of partial derivative polynomials of degree six" @default.
- W1991223639 doi "https://doi.org/10.1063/1.4887661" @default.
- W1991223639 hasPublicationYear "2014" @default.
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