We introduce -adic exponential sums associated to a Laurent polynomial . They interpolate all classical -power order exponential sums associated to . We establish the Hodge bound for the Newton polygon of -functions of -adic exponential sums. This bound enables us to determine, for all , the Newton polygons of -functions of -power order exponential sums associated to an that is ordinary for . We also study deeper properties of -functions of -adic exponential sums. Along the way, we discuss new open problems about the -adic exponential sum itself.
"T-adic exponential sums over finite fields." Algebra Number Theory 3 (5) 489 - 509, 2009. https://doi.org/10.2140/ant.2009.3.489