ON THE CARDINALITY OF THE SET OF SOLUTIONS TO CONGRUENCE EQUATION ASSOCIATED WITH CUBIC FORM
Let be a vector in the space with field of rational numbers and qbe a positive integer, fa polynomial in with coefficient in The exponential sum associated with fis defined as where the sum is taken over a complete set of residues modulo q. The value of depends on the estimate of cardinality the number of elements contained in the set where is the partial derivative of with respect to In this paper, we will discuss the cardinality of the set of solutions to congruence equation associated with a complete cubic by using Newton polyhedron technique. The polynomial is of the form
exponential sums, cardinality, p-adic sizes, Newton polyhedron.