On Root Numbers Connected with Special Values ofL-Functions over imageq(T) Original Research Article

In this paper we give a few explicit formulae for the dual coefficients and some of the root numbers appearing in the expression ofL-functions over imageq(T) ass=1. From these formulae we show that the set of root numbers includes all the basic Gauss sums defined by Thakur as a proper subset. We also prove some properties of the root numbers. Finally, we provide an example which strongly suggests that there is a close relation between root numbers and the general Gauss sums.