Cohomology of quaternionic Shimura varieties at parahoric levels

 Some semi-simple L-functions which are associated with the cohomology of a quaternionic Shimura variety are compared with semi-simple automorphic L-functions. Assuming a certain purity condition this yields a similar result for the usual L-functions. The main theorem of the present paper extends previous results of the author to a more general case. Received: 19 July 2000