  We present a lattice calculation of the hadronic vacuum polarization and the
lowest-order hadronic contribution to the muon anomalous magnetic moment, a_\mu
= (g-2)/2, using 2+1 flavors of improved staggered fermions. A precise fit to
the low-q^2 region of the vacuum polarization is necessary to accurately
extract the muon g-2. To obtain this fit, we use staggered chiral perturbation
theory, including the vector particles as resonances, and compare these to
polynomial fits to the lattice data. We discuss the fit results and associated
systematic uncertainties, paying particular attention to the relative
contributions of the pions and vector mesons. Using a single lattice spacing
ensemble (a=0.086 fm), light quark masses as small as roughly one-tenth the
strange quark mass, and volumes as large as (3.4 fm)^3, we find a_\mu^{HLO} =
(713 \pm 15) \times 10^{-10} and (748 \pm 21) \times 10^{-10} where the error
is statistical only and the two values correspond to linear and quadratic
extrapolations in the light quark mass, respectively. Considering systematic
uncertainties not eliminated in this study, we view this as agreement with the
current best calculations using the experimental cross section for e^+e^-
annihilation to hadrons, 692.4 (5.9) (2.4)\times 10^{-10}, and including the
experimental decay rate of the tau lepton to hadrons, 711.0 (5.0)
(0.8)(2.8)\times 10^{-10}. We discuss several ways to improve the current
lattice calculation.
