Generic twisted $T$-adic exponential sums of polynomials

Chunlei Liu, Chuanze Niu

Published 2009-11-22, updated 2009-12-08Version 2

The twisted $T$-adic exponential sum associated to a polynomial in one variable is studied. An explicit arithmetic polygon is proved to be the generic Newton polygon of the twisted $C$-function of the T-adic exponential sum. It gives the generic Newton polygon of the twisted $L$-functions of $p^m$-power order exponential sums, for all $m$.