A method of estimating the p-adic sizes polynomials - Sapar, Siti Hasana; Aminudin, Siti Syaheera; Mohd Atan, Kamel Ariffin (North Atlantic Univeristy Union, 2014)
The exponential sum associated with f is defined as S (f; q) = ∑x mod 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 in the set V = {x mod q|fx  0 mod q} where fx is the partial derivatives of f with respect to x. In order to determine the cardinality, the p-adic sizes of common zeros of the partial derivative polynomials need to be obtained. This paper will give an estimation of the p-adic sizes of common zeros of partial derivative polynomials of degree eight in p by using Newton polyhedron technique.