A Bessel δ-Method and Hybrid Bounds for GL2. (20th November 2021) - Fan, Yilan; Sun, Qingfeng
Abstract: Let g be a primitive holomorphic or Maass newform for $Γ_0(D)$ . 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 $$\begin{eqnarray*} L\left(1/2+it, g\otimes χ\right)\ll_{g, ε} (q(1+|t|))^{ε}q^{3/8}(1+|t|)^{1/3} \end{eqnarray*}$$ for any ε > 0, where $χ \bmod q$ is a primitive Dirichlet character with q prime and $(q, D)=1$ . This improves the previous known result.