标题： Hecke算子和高亏格中Rankin引理的显式公式 显示英文标题

标题： Explicit formulas for Hecke operators and Rankin's lemma in higher genus

摘要： 我们开发了在球坐标下高亏格Hecke算子的显式公式。 应用到局部Hecke代数和这些代数张量积中的系数的各种生成级数的求和。 特别是，我们在二亏格情况下提出了并证明了Rankin引理。 使用Ikeda-Miyawaki构造，给出了从(GSp2 \times GSp2)到GSp4的提升应用。 显示英文摘要

摘要： We develop explicit formulas for Hecke operators of higher genus in terms of spherical coordinates. Applications are given to summation of various generating series with coefficients in local Hecke algebra and in a tensor product of such algebras. In particular, we formulate and prove Rankin's lemma in genus two. An application to a lifting from (GSp2 \times GSp2) to GSp4 is given using Ikeda-Miyawaki constructions.