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In this paper we prove some non-solvable base change for Hilbert modular representations, and we use this result to show the meromorphic continuation to the entire complex plane of the zeta functions of some twisted quaternionic Shimura varieties. The zeta functions of the twisted quaternionic Shimura varieties are computed at all places.

Non-solvable base change for Hilbert modular representations and zeta functions of twisted quaternionic Shimura varieties