The twisted T-adic exponential sums associated to a polynomial in one variable are studied.An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the C-function of the twisted T-adic exponential sums.This bound gives lower bounds for the Newton polygon of the L-function of twisted p-power order exponential sums.
LIU ChunLei1,& LIU WenXin2,3 1Department of Mathematics,Shanghai Jiao Tong University,Shanghai 200240,China
The twisted T -adic exponential sum associated with xd + λx is studied. If λ = 0, then an explicitarithmetic polygon is proved to be the Newton polygon of the C-function of the twisted T-adic exponential sum.It gives the Newton polygons of the L-functions of twisted p-power order exponential sums.
The generic Newton polygon of L-functions associated with the exponential sums of poly- nomials of degree 3 in two variables is studied by Dwork＇s analytic methods. Wan＇s conjecture is shown to be true for this case.
