2022/06/13 by Hidenori Katsurada, Henry H. Kim, Katsurada, Hidenori +1
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2206.05969
openalex publication_date 2022/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For two Hecke eigenforms h1 and h2 in the Kohnen plus space of half-integral weight, let In(h1) and In(h2) be the Duke-Imamoglu-Ikeda lift of h1 and h2, respectively, which are Siegel cusp forms with respect to Spn(\ZZ). Moreover, let En/2+1/2 be the Cohen Eisenstein series of weight n/2+1/2. We then express the Rankin-Selberg convolution R(s,In(h1),In(h2)) of In(h1) and In(h2) in terms of a certain Dirichlet series D(s,h1,h2,En/2+1/2), which is similar to the triple convolution product of h1, h2 and En/2+1/2. We apply our formula to mass equidistribution for the Duke-Imamoglu-Ikeda lift assuming the holomorphy of D(s,h1,h1,En/2+1/2).