Penganggaran Saiz p-Adic Pensifar Sepunya Terbitan Separa Polinomial Berdarjah Enam

It is known that the value of the exponential sum S(f;pa) depends on the estimate of the cardinality |V|, the number of elements contained in the set V={x mod p^α :f_xΞ 0 mod p^α}where is the partial derivatives of f with respect to . The cardinality of V in turn depends on the p-adic sizes of common zeros of the partial derivatives . This paper presents a method of determining the p-adic sizes of the components of (ξ,η) a common root of partial derivative polynomials of f(x,y) in Z_P(X,Y)of degree six based on the p-adic Newton polyhedron technique associated with the polynomial. The degree six polynomial is of the form F(X,Y)=AX6+BX5Y+CX4Y2+DX3Y3+EX2Y4+MXY5+NY5+SX+TY+K The estimate obtained is in terms of the p-adic sizes of the coefficients of the dominant terms in f.