A Bessel δ-Method and Hybrid Bounds for GL2. (20th November 2021)

• Record Type: Journal Article
• Authors: Fan, Yilan; Sun, Qingfeng
• Is Part Of: Quarterly journal of mathematics. Volume 73:Part 2(2022)
• Page Start: 617
• Page End: 656
• Publication Date: 2021-11-20
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/qmath/haab046
• Languages: English
• ISSNs: 0033-5606

Abstract

Abstract: Let g be a primitive holomorphic or Maass newform for $\Gamma_0(D)$ . In this paper, by studying the Bessel integrals associated with g, we prove an asymptotic Bessel δ -identity associated with g . Among other applications, we prove the following hybrid subconvexity bound $$\begin{eqnarray*} L\left(1/2+it, g\otimes \chi\right)\ll_{g, \varepsilon} (q(1+|t|))^{\varepsilon}q^{3/8}(1+|t|)^{1/3} \end{eqnarray*}$$ for any ε > 0, where $\chi \bmod q$ is a primitive Dirichlet character with q prime and $(q, D)=1$ . This improves the previous known result.