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

TL;DR

This paper establishes subconvexity bounds for automorphic L-functions on GL(2) over number fields, achieving power-saving error terms that break convexity at non-archimedean places.

Contribution

It introduces a spectral identity approach to derive asymptotics with power-saving error terms for second moments, advancing subconvexity results in the depth aspect.

Findings

Power-saving error term breaks convexity at non-archimedean places

Asymptotics obtained for second moments of automorphic L-functions

Applicable to arbitrary number fields and twists by ramified idele characters

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.