论文标题
兰金·塞尔伯格（Rankin-Selberg）
Rankin-Selberg convolution for the Duke-Imamoglu-Ikeda lift
论文作者
论文摘要
For two Hecke eigenforms $h_1$ and $h_2$ in the Kohnen plus space of half-integral weight, let $I_n(h_1)$ and $I_n(h_2)$ be the Duke-Imamoglu-Ikeda lift of $h_1$ and $h_2$, respectively, which are Siegel cusp forms with respect to $Sp_n(\ZZ)$.此外，令$ e_ {n/2+1/2} $为Cohen Eisenstein系列均为$ n/2+1/2 $。然后，我们表达$ i_n（H_1）$和$ i_n（h_1）$和$ i_n（h_2）$的Rankin-Selberg卷积$ r（s，i_n（i_n（h_1），i_n（h_2））$在某个dirichlet $ d（s，h_1，h_1，h_1，h_2，e_2，e_ {n/2+1+1/2} $ hh tr tr tr tr tr y_1，h_2）$中$ e_ {n/2+1/2} $。我们将公式应用于duke-imamoglu-ikeda升降机的质量分布，假设$ d（s，h_1，h_1，e_ {n/2+1/2}）$的holomorphy $。
For two Hecke eigenforms $h_1$ and $h_2$ in the Kohnen plus space of half-integral weight, let $I_n(h_1)$ and $I_n(h_2)$ be the Duke-Imamoglu-Ikeda lift of $h_1$ and $h_2$, respectively, which are Siegel cusp forms with respect to $Sp_n(\ZZ)$. Moreover, let $E_{n/2+1/2}$ be the Cohen Eisenstein series of weight $n/2+1/2$. We then express the Rankin-Selberg convolution $R(s,I_n(h_1),I_n(h_2))$ of $I_n(h_1)$ and $I_n(h_2)$ in terms of a certain Dirichlet series $D(s,h_1,h_2,E_{n/2+1/2})$, which is similar to the triple convolution product of $h_1, h_2$ and $E_{n/2+1/2}$. We apply our formula to mass equidistribution for the Duke-Imamoglu-Ikeda lift assuming the holomorphy of $D(s,h_1,h_1,E_{n/2+1/2})$.
