Faculty Publications
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.
Department
Department of Mathematics
Original Publication Date
1-1-2000
DOI of published version
10.1007/PL00010088
Recommended Citation
Choie, Young Ju and Lee, Min Ho, "Mixed Siegel Modular Forms And Special Values Of Certain Dirichlet Series" (2000). Faculty Publications. 3673.
https://scholarworks.uni.edu/facpub/3673
