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

Abstract

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