English

Subconvexity for modular form L-functions in the t aspect

Number Theory 2021-08-09 v3

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.

Keywords

Cite

@article{arxiv.1707.01576,
  title  = {Subconvexity for modular form L-functions in the t aspect},
  author = {Andrew R. Booker and Micah B. Milinovich and Nathan Ng},
  journal= {arXiv preprint arXiv:1707.01576},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-22T20:39:07.624Z