Twisted exponential sums of polynomials in one variable

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.