Generic Exponential Sums Associated To Polynomials Of Degree 3 In Two Variables

In this paper we give an explicit description of the generic Newton polygon of Lfunctionsassociated to the exponential sums of polynomials of degree 3 in two variables. We prove that there is a Zariski dense open subset U defined over Q such that for every geometric point f(x) in U(Q) such that the Newton polygon of L~*(f(x) mod p,t) is the generic Newton polygon if and only if f(x)∈U(Q). We show Wan's conjecture for this case, that is the generic Newton polygon goes to its Hodge polygon as p goes to infinity.