Level aspect subconvexity for \textrmGL(2)× \textrmGL(2) \textrmL-functions

2024/12/16 by Keshav Aggarwal, S. Jay Kumar, Aggarwal, Keshav +9
Mathematics · #11F66 #11M41 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2412.12410

openalex publication_date 2024/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be a newform of prime level p with any central character χ (\bmod p), and let g be a fixed cusp form or Eisenstein series for \hboxSL₂(ℤ). We prove the subconvexity bound: for any ε>0, L(1/2, f ⊗ g) ≪ p^1/2-1/524+ε, where the implied constant depends on g, ε, and the archimedean parameter of f. This improves upon the previously best-known result by Harcos and Michel. Our method ultimately relies on non-trivial bounds for bilinear forms in Kloosterman fractions pioneered by Duke, Friedlander, and Iwaniec, with later innovations by Bettin and Chandee.

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