What are the best (portable) cross-platform arbitrary-precision math libraries?

Overall, he fastest general purpose arbitrary precision library is GMP. If you want to work with floating point values, look at the the MPFR library. MPFR is based on GMP.

Regarding native arbitrary precision support in other languages, Python uses its own implementation because of license, code size, and code portability reasons. The GMPY module lets Python access the GMP library.

GMP is the popular choice. Squeak Smalltalk has a very nice library, but it's written in Smalltalk.

You asked for relevant books or articles. The tricky part of bignums is long division. I recommend Per Brinch Hansen's paper Multiple-Length Division Revisited: A Tour of the Minefield.