Subconvexity for modular form L-functions in the t aspect

TL;DR

This paper proves a subconvexity bound for L-functions of modular forms in the t aspect, resolving a 35-year-old open problem by extending Voronoi summation techniques to all levels.

Contribution

It introduces a generalized Voronoi summation method applicable to all levels, enabling the proof of a subconvexity estimate comparable to Good's bound.

Findings

Established a t aspect subconvexity bound for modular form L-functions

Extended Voronoi summation to non-squarefree levels

Resolved a long-standing open problem in the field

Abstract

Modifying a method of Jutila, we prove a t aspect subconvexity estimate for L-functions associated to primitive holomorphic cusp forms of arbitrary level that is of comparable strength to Good's bound for the full modular group, thus resolving a problem that has been open for 35 years. A key innovation in our proof is a general form of Voronoi summation that applies to all fractions, even when the level is not squarefree.