论文标题
在$ p $ -adic $ l $ - for $ \ operatoTorname {gl}（2）（2）\ times \ permatatorname {gl}（3）（3）$ saito-kurokawa lifts
On $p$-adic $L$-functions for $\operatorname{GL}(2)\times\operatorname{GL}(3)$ via pullbacks of Saito--Kurokawa lifts
论文作者
论文摘要
我们构建了一个单变量的$ p $ -Adic $ l $ - 功能附有两个普通$ p $ p $稳定的新形式的$ \ mathbf {f} $，$ \ mathbf {g} $，插入复杂$ l $ -series $ l（f fimme）的代数部分的代数部分，当$ f $和$ g $范围比$ \ mathbf {f} $的经典专业范围内，$ \ mathbf {g} $在合适的重量空间线上。该施工取决于两个主要结果：相关复杂的中央$ l $值的明确公式，以及非繁琐的$λ$ - $ -ADIC SHINTANI升降机和Saito-saito-kurokawa升降机在以前的作品中研究了。我们还说明，在适当的符号假设下，此$ p $ -adic $ l $ - 功能是三型$ p $ -p $ -adic $ l $ -function的因素，该因素附加到$ \ m m mathbf {f} $，$ \ mathbf {g}
We build a one-variable $p$-adic $L$-function attached to two Hida families of ordinary $p$-stabilised newforms $\mathbf{f}$, $\mathbf{g}$, interpolating the algebraic part of the central values of the complex $L$-series $L(f \otimes \textrm{Ad}(g), s)$ when $f$ and $g$ range over the classical specialisations of $\mathbf{f}$, $\mathbf{g}$ on a suitable line of the weight space. The construction rests on two major results: an explicit formula for the relevant complex central $L$-values, and the existence of non-trivial $Λ$-adic Shintani liftings and Saito--Kurokawa liftings studied in a previous work by the authors. We also illustrate that, under an appropriate sign assumption, this $p$-adic $L$-function arises as a factor of a triple product $p$-adic $L$-function attached to $\mathbf{f}$, $\mathbf{g}$, and $\mathbf{g}$.
