On an error term for the first moment of twisted L-functions

2022/01/26 by Xinyi He, He, Xinyi
Mathematics · Social Sciences · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Historical Geopolitical and Social Dynamics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2201.10891

openalex publication_date 2022/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be a Hecke-Maass cusp form for the full modular group and let χ be a primitive Dirichlet character modulo a prime q. Let s₀=σ₀+it₀ with (1)/(2)≤σ₀<1. We improve the error term for the first moment of L(s₀,f⊗χ)L(s₀,χ) over the family of even primitive Dirichlet characters. As an application, we show that for any t∈ℝ, there exists a primitive Dirichlet character χ modulo q for which L(1/2+it,f⊗χ)L(1/2+it,χ)≠0 if the prime q satisfies q≫ (1+|t|)^{(543)/(25)+ε}.

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