Structures and dimensions of vector valued Jacobi forms of degree two
type: Item
instance of: scholarly article
title: Structures and dimensions of vector valued Jacobi forms of degree two
zbMATH Open document ID: 1396.11076
DOI: 10.4171/PRIMS/163
author: Tomoyoshi Ibukiyama
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2015-09-21T00:00:00Z
review text: Summary: We give a complete characterization of vector valued holomorphic Jacobi forms of degree two of index one in the sense of Ziegler by the Taylor expansion and vector valued Siegel modular forms of various weights. By this characterization, we also give explicit dimension formulas for spaces of vector valued holomorphic Jacobi forms of index one of degree two, using those for vector valued Siegel modular forms and a certain surjectivity theorem on the Witt operator (the restriction operator to the diagonals). Our characterization also gives a concrete way to give the plus subspace of the space of Siegel modular forms of half-integral weight.
Mathematics Subject Classification ID: 11F50
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11F37
zbMATH DE Number: 6483951
zbMATH Keywords: Jacobi forms
zbMATH Keywords: Siegel modular forms
zbMATH Keywords: dimension formula
zbMATH Keywords: half-integral weight
MaRDI profile type: Publication
cites work: Vector valued Siegel's modular forms of degree two and the associated Andrianov \(L\)-functions
cites work: A decomposition theorem for Jacobi forms
cites work: The theory of Jacobi forms
cites work: A vanishing theorem for automorphic forms of Siegel's modular group
cites work: Q3963086
cites work: Siegel modular forms of half integral weight and a lifting conjecture
cites work: Q4272876
cites work: Q4253166
cites work: A conjecture on a Shimura type correspondence for Siegel modular forms, and Harder's conjecture on congruences
cites work: Taylor expansions of Jacobi forms and applications to explicit structures of degree two
cites work: Vector valued Siegel modular forms of symmetric tensor weight of small degrees
cites work: Q5250509
cites work: Q5852624
cites work: Q3677818
cites work: An explicit dimension formula for the spaces of generalized automorphic forms with respect to \(\mathrm{Sp}(2, \mathbb Z)\)
cites work: Q4505544
cites work: Dimension formulas for spaces of vector-valued Siegel cusp forms of degree two
cites work: Jacobi forms of higher degree
description: scientific article; zbMATH DE number 6483951