Abstract:

Considering the L-function of exponential sums associated to a polynomial over a finite field F_q,  we proved that there are only finitely many possible forms of Newton polygons for the L-function of degree d polynomial independent of p, when p is larger than a constant D*(depend on d only), i.e., a reciprocal root's p-adic order has form (up-v)/(p-1)D* in which u/D*, v/D* have finitely many possible values. Furthermore, when p>D*, to determine the Newton polygon is only to determine it for any two specified primes p_1, p_2>D* in the same residue class of D*.