  Dwork's conjecture, now proven by Wan, states that unit root L-functions
"coming from geometry" are p-adic meromorphic. In this paper we study the
p-adic variation of a family of unit root L-functions coming from a suitable
family of toric exponential sums. In this setting, we find that the unit root
L-functions each have a unique p-adic unit root. We then study the variation of
this unit root over the family of unit root L-functions. Surprisingly, we find
that this unit root behaves similarly to the classical case of families of
exponential sums. That is, the unit root is essentially a ratio of
A-hypergeometric functions.
