2018/07/18 by Henry H. Kim, Kim, Henry H., Takuya Yamauchi +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1807.06791
14 pages
arxiv created 2018/07/18 · arxiv updated 2018/07/19
Miyawaki type lifts are kinds of Langlands functorial lifts and a special case was first conjectured by Miyawaki and proved by Ikeda for Siegel cusp forms. Since then, such a lift for Hermitian modular forms was constructed by Atobe and Kojima , and for half-integral weight Siegel cusp forms by Hayashida, and we constructed Miyawaki type lift for \rm GSpin(2,10). Recently Ikeda and Yamana generalized Ikeda type construction and accordingly did Miyawaki type lift for Hilbert cusp forms in a remarkable way. In all these works, a construction of Miyawaki type lift takes two steps as follows: First, construct Ikeda type lift on a bigger group from an elliptic cusp form, and then define a certain integral on a block diagonal element which is an analogue of pull-back formula studied by Garrett for Siegel Eisenstein series. If the integral is non-vanishing, we show that it is a Hecke eigen cusp form, and it is the Miyawaki type lift. The question of non-vanishing of the integral was left open. In this paper, we show the non-vanishing for certain special cases.