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

2006/10/12 by Alexei Panchishkin, Panchishkin, Alexei, Kirill Vankov +1
Mathematics · #11F60 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F60

paper · pdf · doi:10.48550/arxiv.math/0610417

arxiv created 2007/01/05 · arxiv updated 2009/12/01

Abstract

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 × GSp2) to GSp4 is given using Ikeda-Miyawaki constructions.

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