Theta type Jacobi forms

Woitalla, Martin

doi:10.4064/aa161214-26-7

Cited by 5 publications

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“…It was also verified that the Jacobian determinant of the seven modular forms is not zero. We know from [Woi17] that there is a reflective modular form of weight is generated by all 2-reflections, which can not be covered by Lemma 3.4. The structure results in [AI05] can also be verified in a similar way.…”

Section: A Sufficient Condition To Be Free Algebrasmentioning

confidence: 99%

The classification of free algebras of orthogonal modular forms

Wang¹

2020

Preprint

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We prove a necessary and sufficient condition for the graded algebra of automorphic forms on a symmetric domain of type IV to be free. From the necessary condition, we derive a classification result. Let M be an even lattice of signature (2, n) splitting two hyperbolic planes. Suppose Γ is a subgroup of the integral orthogonal group of M containing the discriminant kernel. It is proved that there are exactly 26 groups Γ such that the space of modular forms for Γ is a free algebra. Using the sufficient condition, we recover some well-known results.

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Section: A Sufficient Condition To Be Free Algebrasmentioning

confidence: 99%

The classification of free algebras of orthogonal modular forms

Wang¹

2020

Preprint

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“…, j = 1, 2, 3 which belong to M 8 ( Γ 4 , 1). There is a cusp form∆ 4A1 24 ∈ S 24 (Γ 4 , v π ) The divisor equals the Γ 4 -orbit of D 4 ε1+ε4 .ProofThis function coincides with the cusp form of weight 24 for the lattice D 4 which was constructed in[29, Theorem 4.4]. Since 4A 1 is a sublattice of D 4 we obtain a function with the modular behaviour stated above where the character v π appears due to the definition of ϑ (j)…”

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confidence: 70%

“…In the following we construct three modular form with respect to the character v π . Following [29] we consider the following three theta type Jacobi forms with respect to the coordinates introduced in ( 2)…”

Section: Proofmentioning

confidence: 99%

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Modular forms for the $A_{1}$-tower

Woitalla¹

2017

Preprint

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In the 1960's Igusa determined the graded ring of Siegel modular forms of genus two. He used theta series to construct χ 5 , the cusp form of lowest weight for the group Sp(2, Z). In 2010 Gritsenko found three towers of orthogonal type modular forms which are connected with certain series of root lattices. In this setting Siegel modular forms can be identified with the orthogonal group of signature (2, 3) for the lattice A 1 and Igusa's form χ 5 appears as the roof of this tower. We use this interpretation to construct a framework for this tower which uses three different types of constructions for modular forms. It turns out that our method produces simple coordinates.

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“…It was also verified that the Jacobian determinant of the seven modular forms is not zero. We know from [Woi17] that there is a reflective modular form of weight 24 on whose divisor is a sum of for all with and . In view of the isomorphisms this reflective modular form can be regarded as a 2-reflective modular form on .…”

Section: A Sufficient Condition To Be Free Algebrasmentioning

confidence: 99%

The classification of free algebras of orthogonal modular forms

Wang¹

2021

Compositio Math.

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We prove a necessary and sufficient condition for the graded algebra of automorphic forms on a symmetric domain of type IV being free. From the necessary condition, we derive a classification result. Let $M$ be an even lattice of signature $(2,n)$ splitting two hyperbolic planes. Suppose $\Gamma$ is a subgroup of the integral orthogonal group of $M$ containing the discriminant kernel. It is proved that there are exactly 26 groups $\Gamma$ such that the space of modular forms for $\Gamma$ is a free algebra. Using the sufficient condition, we recover some well-known results.

show abstract

Theta type Jacobi forms

Cited by 5 publications

References 0 publications

The classification of free algebras of orthogonal modular forms

The classification of free algebras of orthogonal modular forms

Modular forms for the $A_{1}$-tower

The classification of free algebras of orthogonal modular forms

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