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From a spectral identity we obtain asymptotics with error term for the secondintegral moments of families of automorphic L-functions for GL(2) over anarbitrary number field according to twists by idele characters with arbitraryramification at a fixed finite place. The power-saving in the error term breaksconvexity at this non-archimedean place.

Subconvexity bounds in depth-aspect for automorphic L-functions on GL(2)