Collinear and soft-gluon corrections to Higgs production at next-to-next-to-next-to-leading order

I present analytical expressions for the collinear and soft-gluon corrections to Higgs production via the process b (b) over bar -> H as well as gg -> H through next-to-next-to-next-to-leading order (NNNLO). The soft corrections are complete, while the collinear corrections include leading and some subleading logarithms. Numerical results at the Tevatron and the CERN LHC are presented, primarily for b (b) over bar -> H. It is shown that the collinear terms greatly improve the soft and virtual approximation at next-to-leading order and next-to-next-to-leading order, especially when subleading terms are included. The NNNLO collinear and soft corrections provide significant enhancements to the total cross section. I also provide expressions for the collinear and soft corrections through NNNLO for the related Drell-Yan process.