Linux build documentation is mostly geared towards Ubuntu 14.04 (LTS).
Appropriate package is called `libgmp-dev` there.

Note that on pristine installations building `geth` with godep will
fail because this header is missing. This is not documented in the
top-level README, but is on the wiki:

https://github.com/ethereum/go-ethereum/wiki/Installation-Instructions-for-Ubuntu#building-geth-command-line-client

That page recommends `libgmp3-dev`, which ATM provides same version
as `libgmp-dev`.