论文标题
$ \ rm gl_2 \ times gl_2 $ $ $ $ l $ - for tepth in tepth方面的界限
Bounds for $\rm GL_2\times GL_2$ $L$-functions in depth aspect
论文作者
论文摘要
令$ f $和$ g $为$ \ rm sl_2（\ m athbb {z}）$的holomorphic或maass cusp表格，让$χ$是Prime Power导体$ \ Mathfrak {Q} = P^κ$ at $ p $ Prime和$κ> $κ> 12 $的原始的dirichlet特性。 Rankin-selberg $ l $ functions $ l（s，f \ otime g \ otimesχ）$绑定的子概标在深度$$ l \ left（\ frac {1} {1} {2}，f \ otimime g \ outime g c \ up g g e e}中证明了。 p^{3/4} \ Mathfrak {q}^{15/16+\ varepsilon}。 $$
Let $f$ and $g$ be holomorphic or Maass cusp forms for $\rm SL_2(\mathbb{Z})$ and let $χ$ be a primitive Dirichlet character of prime power conductor $\mathfrak{q}=p^κ$ with $p$ prime and $κ>12$. A subconvex bound for the central values of the Rankin-Selberg $L$-functions $L(s,f\otimes g \otimes χ)$ is proved in the depth-aspect $$ L\left(\frac{1}{2},f\otimes g \otimes χ\right)\ll_{f,g,\varepsilon} p^{3/4}\mathfrak{q}^{15/16+\varepsilon}. $$
