Generic T-adic exponential sums in one variable

Chunlei Liu, Wenxin Liu, Chuanze Niu

Published 2009-01-04, updated 2009-11-03Version 6

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