论文标题
$ \ mathrm {gl} _2 $
A Bessel $δ$-method and hybrid bounds for $\mathrm{GL}_2$
论文作者
论文摘要
令$ g $为$γ_0（d）$的原始全体形态或maass Newform。在本文中，通过研究与$ g $相关的贝塞尔积分，我们证明了与$ g $相关的渐近贝塞尔$δ$ - 身份。在其他应用程序中，我们证明了以下混合子概率绑定$$ l \ left（1/2+it，g \ otimesχ\ right）\ ll_ {g，\ varepsilon}（q（q（q（1+ | t | t |））^{\ varepsilon} $ \ varepsilon> 0 $，其中$χ\ bmod q $是一个原始的dirichlet字符，$（q，d）= 1 $。这改善了先前的已知结果。
Let $g$ be a primitive holomorphic or Maass newform for $Γ_0(D)$. In this paper, by studying the Bessel integrals associated to $g$, we prove an asymptotic Bessel $δ$-identity associated to $g$. Among other applications, we prove the following hybrid subconvexity bound $$ L\left(1/2+it,g\otimes χ\right)\ll_{g,\varepsilon} (q(1+|t|))^{\varepsilon}q^{3/8}(1+|t|)^{1/3} $$ for any $\varepsilon>0$, where $χ\bmod q$ is a primitive Dirichlet character with $(q, D)=1$. This improves the previous known result.
