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 eqnarray* L(1/2+it, gχ)_g, ε (q(1+|t|))^εq^3/8(1+|t|)^1/3 eqnarray* for any ε > 0, where χ q is a primitive Dirichlet character with q prime and (q, D)=1 . This improves the previous known result.