  The L-function of symmetric powers of classical Kloosterman sums is a
polynomial whose degree is now known, as well as the complex absolute values of
the roots. In this paper, we provide estimates for the p-adic absolute values
of these roots. Our method is indirect. We first develop a Dwork-type p-adic
cohomology theory for the two-variable infinite symmetric power L-function
associated to the Kloosterman family, and then study p-adic estimates of the
eigenvalues of Frobenius. A continuity argument then provides the desired
p-adic estimates.
