On L-functions of twisted T-adic exponential sums

Let f(x)=∑v∈Iavxv∈Fq[x1±1,x2±1,⋯,xn±1] with I∈Zn be a nonconstant Laurent polynomial in n-variables. Twisted T-adic exponential sums associated to f are studied. The lower bound of the T-adic Newton polygon of the characteristic function Cf,u(s,T) is established. When n=1 and f(x) is a polynomial of degree d, firstly, we show the T-adic Newton polygon of Cf,u(s,T) enjoys some stable and ordinary properties at the points whose abscissas are kd,k∈N and then we show the Newton slopes of the twisted L-function Lf,u(s,πm) are independent of m when m is large enough. As a consequence, we also show the Newton slopes of Lf,u(s,T) form arithmetic progressions which generalize the result of Davis-Wan-Xiao to the twisted case.