Lowest weight modules of \(\mathrm{Sp}_4 (\mathbb{R})\) and nearly holomorphic Siegel modular forms

DOI10.1215/21562261-2021-0012zbMath1485.11089arXiv1501.00524OpenAlexW3187017565MaRDI QIDQ824272

Ralf Schmidt, Abhishek Saha, Ameya Pitale

Publication date: 15 December 2021

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.00524

zbMATH Keywords

representation theorySiegel modular forms

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items

Nearly holomorphic automorphic forms on \(\mathrm{SP}_{2n}\) with sufficiently regular infinitesimal characters and applications ⋮ The special values of the standard 𝐿-functions for 𝐺𝑆𝑝_{2𝑛}×𝐺𝐿₁ ⋮ Almost holomorphic Poincaré series corresponding to products of harmonic Siegel-Maass forms ⋮ Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level ⋮ Genus two Siegel quasi-modular forms and Gromov-Witten theory of toric Calabi-Yau threefolds ⋮ AUTOMORPHIC SL ₂ ‐PERIODS AND THE SUBCONVEXITY PROBLEM FOR GL ₂ × GL ₃ ⋮ Constructions of nearly holomorphic Siegel modular forms of degree two ⋮ Pullback formulae for nearly holomorphic Saito-Kurokawa lifts ⋮ AN EQUIDISTRIBUTION THEOREM FOR HOLOMORPHIC SIEGEL MODULAR FORMS FOR AND ITS APPLICATIONS ⋮ Integrality and cuspidality of pullbacks of nearly holomorphic Siegel Eisenstein series ⋮ Nearly overconvergent Siegel modular forms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Lie theory of certain modular form and arithmetic identities
• Modular forms of genus 2 and weight 1
• Pullbacks of Eisenstein series from \(\text{GU}(3,3)\) and critical \(L\)-values for \(\text{GSp}(4) \times \text{GL}(2)\)
• Combinatorics of Maass-Shimura operators
• Hermitian symmetric spaces and their unitary highest weight modules
• On certain vector valued Siegel modular forms of degree two
• Eisenstein series on Shimura varieties
• On a class of nearly holomorphic automorhic forms
• Arithmetic vector bundles and automorphic forms on Shimura varieties. I
• A multiplicity one theorem for holomorphically induced representations
• Nearly holomorphic functions on Hermitian symmetric spaces
• On Hilbert modular forms of half-integral weight
• A note on three lemmas of Shimura
• Differential operators, holomorphic projection, and singular forms
• Non-Archimedean \(L\)-functions and arithmetical Siegel modular forms
• \(p\)-adic measures attached to Siegel modular forms
• A note on the growth of nearly holomorphic vector-valued Siegel modular forms
• An intrinsic analysis of unitarizable highest weight modules
• On ratios of Petersson norms for Yoshida lifts
• On algebraicity of vector valued Siegel modular forms
• Critical values of \(L\)-functions on \(\text{GSp}_2 \times \text{GL}_2\)
• Siegel's modular forms and Dirichlet series. Course given at the University of Maryland, 1969-1970
• The CAP representations of GSp (4,).
• Intertwining operators and composition series of generalized and degenerate principal series for Sp(4,R)
• Vektorwertige Siegelsche Modulformen kleinen Gewichtes.
• Multiplicity free categories of highest weight representations
• Nearly Overconvergent Modular Forms
• ON MODULAR FORMS FOR THE PARAMODULAR GROUPS
• Siegel modular forms and representations