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

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

2006-10-12

arxiv.org/abs/math/0610417v5

Mathematics

Number Theory

Scientific paper

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.

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