Subconvexity for modular form L-functions in the t aspect

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.

minor revisions; to appear in Adv. Math.; 30 pages

References in corpus (2)

• Quantitative estimates for simple zeros of L-functions
• Sub-Weyl bounds for $GL(2)$ $L$-functions

Cited by in corpus (9)

• Quantitative estimates for simple zeros of L-functions
• Sub-Weyl bounds for $GL(2)$ $L$-functions
• Uniform Titchmarsh divisor problems
• Adelic Voronoi Summation and Subconvexity for GL(2) L-Functions in the depth Aspect
• Counting integer points on quadrics with arithmetic weights
• Weyl bound for $\mathrm{GL}(2)$ in $t$-aspect via a trivial delta method
• Hybrid Weyl-type bound for $p$-power twisted $\mathrm{GL}(2)$ $L$-functions
• GL(2) Weyl Bound via a multiplicative character delta method
• A Bessel delta-method and exponential sums for GL(2)