Subconvexity for \rm GL₂ × GL₂ L-functions in the depth aspect

2025/02/26 by Tengyou Zhu, Zhu, Tengyou
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2502.18727

openalex publication_date 2025/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f and g be holomorphic or Maass cusp forms for \rm SL₂(ℤ) and let χ be a primitive Dirichlet character of prime power conductor q=pⁿ. For any given ε>0, we establish the following subconvexity bound L(1/2,f⊗ g ⊗ χ)≪_f,g,εq^9/10+ε. The proof employs the DFI circle method with standard manipulations, including the conductor-lowering mechanism, Voronoi summation, and Cauchy--Schwarz inequality. The key input is certain estimates on the resulting character sums, obtained using the p-adic version of the van der Corput method.

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