  The Lya forest in quasar spectra probes scales where massive neutrinos can
strongly suppress the growth of mass fluctuations. Using hydrodynamic
simulations with massive neutrinos, we successfully test techniques developed
to measure the mass power spectrum from the forest. A recent observational
measurement in conjunction with a conservative implementation of other
cosmological constraints places upper limits on the neutrino mass: m_nu < 5.5
eV for all values of Omega_m, and m_nu < 2.4 (Omega_m/0.17 -1) eV, if 0.2 <
Omega_m <0.5 as currently observationally favored (both 95 % C.L.).
