Subconvexity bounds for automorphic<i>L</i>-functions

Abstract

Abstract We break the convexity bound in the t -aspect for L -functions attached to cusp forms f for GL 2 ( k ) over arbitrary number fields k . The argument uses asymptotics with error term with a power saving, for second integral moments over spectral families of twists L ( s,f ⊗χ) by Grossencharacters χ, from our previous paper on integral moments.