**Title of Talk**: Holomorphy of symmetric cube L-functions for GL(2)

In this talk which is based on a joint work with Henry Kim, I will sketch a proof of our recent result on the holomorphy of symmetric cube L-functions for GL(2). More precisely, I will show that the full L-function attached to every non-monomial cusp form on GL(2) of the adeles of a number field and the four dimensional irreducible symmetric cube representation of the L-group GL(2,C) of GL(2) is entire. The case of monomial cusp forms, where there are poles, is well-known.