arXiv:1207.6177 Hasse-Weil zeta functions of SL_2-character varieties of arithmetic two bridge link complements fra arXiv Front: math.NT av Shinya Harada Hasse-Weil zeta functions of SL_2-character varieties of arithmetic two bridge link groups are determined
Special values of the zeta functions at s=0,1,2 are also investigated.
arXiv:1003.2451 The Langlands-Kottwitz approach for some simple Shimura Varieties from arXiv Front: math.AG by Peter Scholze We show how the Langlands-Kottwitz method can be used to determine the semisimple local factors of the Hasse-Weil zeta-function of certain Shimura varieties. On the way, we prove a conjecture of Haines and Kottwitz in this special case.
http://golem.ph.utexas.edu/category/2010/07/zeta_functions_dedekind_versus.html
nLab page on Hasse-Weil zeta function