Faculty Publications

Title

Mixed Siegel modular forms and special values of certain Dirichlet series

Document Type

Article

Keywords

Dirichlet series, Mixed Siegel modular form

Journal/Book/Conference Title

Monatshefte fur Mathematik

Volume

131

Issue

2

First Page

109

Last Page

122

Abstract

Let ø : ℋ nr → ℂ be a Siegel modular form of weight ℓ, and let τσ : ℋ n → ℋ nr be an Eichler embedding, where ℋ n denotes the Siegel upper half space of degree n. We use the notion of mixed Siegel modular forms to construct the linear map ℒ*ø,τσ : script capital L signk+ℓr(N) → script capital L signk(N) of the spaces of Siegel cusp forms for the congruence subgroup Γ0(N) ⊂ Sp(n, ℝ) and express the Fourier coefficients of the image ℒ*ø,τσf of an element f ∈ script capital L signk+ℓr(N) under ℒ*ø,τσ in terms of special values of a certain Dirichlet series. We also discuss connections between mixed Siegel cusp forms and holomorphic forms on a family of abelian varieties.

Original Publication Date

1-1-2000

DOI of published version

10.1007/PL00010088

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