A Bessel δ-Method and Hybrid Bounds for GL2

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 δ-identity g. Among other applications, following hybrid subconvexity bound $$\begin{eqnarray*} L\left(1/2+it,g\otimes \chi\right)\ll_{g,\varepsilon} (q(1+|t|))^{\varepsilon}q^{3/8}(1+|t|)^{1/3} \end{eqnarray*}$$ any ε > 0, where $\chi \bmod q$ is Dirichlet character q prime and $(q, D)=1$. This improves previous known result.