论文标题
$ \ mathrm {gl} _2 \ times \ times \ mathrm {gl} _3 $
Automorphic $\mathrm{SL}_2$-periods and the subconvexity problem for $\mathrm{GL}_2 \times \mathrm{GL}_3$
论文作者
论文摘要
我们证明了针对$ \ mathrm {gl} _2 \ times \ times \ mathrm {gl} _3 $的某些自动形态$ l $ functions of Subconvexity问题的新（条件）结果。这是根据与新Forms $ f $ $ f $和均匀重量和奇数SquareFree级别相关联的新$ \ Mathrm {SL} _2 $ - Period积分的计算。相同的计算也导致$ 6 $复杂$ l $ l $ l $ l $ l（f \ otimes \ mathrm {ad}（g），s）$的中心价值公式，在Arxiv中扩展了以前的工作：1804.02352。
We prove a new (conditional) result towards the subconvexity problem for certain automorphic $L$-functions for $\mathrm{GL}_2 \times \mathrm{GL}_3$. This follows from the computation of new $\mathrm{SL}_2$-period integrals associated with newforms $f$ and $g$ of even weight and odd squarefree level. The same computations also lead to a central value formula for degree $6$ complex $L$-series of the form $L(f \otimes \mathrm{Ad}(g), s)$, extending previous work in arXiv:1804.02352.
