2017/07/31 by Andrew R. Booker, Micah B. Milinovich, Nathan Ng · 22 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Combinatorics #Cusp (singularity) #Cusp form #Geometry #Holomorphic function #Mathematics #Modular form #Pure mathematics #Square-free integer #math.NT
paper · pdf · doi:10.1016/j.aim.2018.10.037
published in Advances in Mathematics 341, 299-335 (Elsevier BV) · minor revisions; to appear in Adv. Math.; 30 pages
arxiv created 2018/10/23 · openalex publication_date 2018/11/01 · arxiv updated 2021/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.