Dwork’s conjecture, now proven by Wan, states that unit root
-functions “coming from
geometry” are
-adic
meromorphic. In this paper we study the
-adic variation of a family
of unit root
-functions
coming from a suitable family of toric exponential sums. In this setting, we find that the unit root
-functions each
have a unique
-adic
unit root. We then study the variation of this unit root over the family of unit root
-functions.
Surprisingly, we find that this unit root behaves similarly to the
classical case of families of exponential sums, as studied by Adolphson
and Sperber (2012). That is, the unit root is essentially a ratio of
-hypergeometric
functions.