We will look at zeta, multizeta and variants taking (transcendental) values in completions of function fields rather than Artin-Weil type zeta (essentially rational functions) in characteristic zero. We discuss results and conjectures on relations they satisfy, independence results and relations to structures such as t-motives, Shtukas, absolute Galois group, Hopf algebras etc.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/246