Structures and dimensions of vector valued Jacobi forms of degree two

DOI10.4171/PRIMS/163zbMath1396.11076MaRDI QIDQ496426

Tomoyoshi Ibukiyama

Publication date: 21 September 2015

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

zbMATH Keywords

Jacobi formshalf-integral weightdimension formulaSiegel modular forms

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Jacobi forms (11F50)

Related Items

Generic differential operators on Siegel modular forms and special polynomials ⋮ One-line formula for automorphic differential operators on Siegel modular forms

Cites Work

• Dimension formulas for spaces of vector-valued Siegel cusp forms of degree two
• Taylor expansions of Jacobi forms and applications to explicit structures of degree two
• The theory of Jacobi forms
• Jacobi forms of higher degree
• An explicit dimension formula for the spaces of generalized automorphic forms with respect to \(\mathrm{Sp}(2, \mathbb Z)\)
• Vector valued Siegel's modular forms of degree two and the associated Andrianov \(L\)-functions
• A vanishing theorem for automorphic forms of Siegel's modular group
• A decomposition theorem for Jacobi forms
• Siegel modular forms of half integral weight and a lifting conjecture
• A conjecture on a Shimura type correspondence for Siegel modular forms, and Harder's conjecture on congruences
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