Mixed Siegel Modular Forms And Special Values Of Certain Dirichlet Series

Authors

Young Ju Choie, Pohang University of Science and TechnologyFollow
Min Ho Lee, University of Northern IowaFollow

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