Geometry and Arithmetic on the Siegel–Jacobi Space

Yang, Jae-Hyun

doi:10.1007/978-3-319-11523-8_10

Cited by 7 publications

(6 citation statements)

References 63 publications

(74 reference statements)

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“…An automorphic form is a function from a topological group G to the complex numbers C which is invariant with respect to some discrete subgroup Γ ⊂ G. In this case, the relevant group on M Normal is the Jacobi group (see [Yan15] for details) and the associated group for…”

Section: Andmentioning

confidence: 99%

A Hall of Statistical Mirrors

Khan¹,

Zhang²

2021

Preprint

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The primary focus of information geometry are statistical manifolds, which are parametrized families of probability measures, induced with the Fisher-Rao metric and a pair of torsion-free conjugate connections. In recent work [ZK20], the authors considered parametrized probability distributions as partially-flat statistical manifolds admitting torsion and showed that there is a complex to symplectic duality on the tangent bundles of such manifolds, based on the dualistic geometry of the underlying manifold.In this paper, we explore this correspondence further in the context of Hessian manifolds, in which case the conjugate connections are both curvature-and torsion-free, and the associated dual pair of spaces are Kähler manifolds. We focus on several key examples and their geometric features. In particular, we show that the moduli space of univariate normal distributions gives rise to a correspondence between the Siegel half-space and the Siegel-Jacobi space, which are spaces that appear in the context of automorphic forms.

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Section: Andmentioning

confidence: 99%

A Hall of Statistical Mirrors

Khan¹,

Zhang²

2021

Preprint

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“…Describe the algebra of all G J -invariant differential operators on H n,m explicitly. We refer to [18,20] for some details.…”

Section: Basic Problems In the Geometry Of The Siegel-jacobi Spacementioning

confidence: 99%

Problems in the Geometry of the Siegel-Jacobi Space

Yang

2019

Preprint

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“…In the special case ρ(A) = (det(A)) k with A ∈ GL(g, C) and a fixed k ∈ Z, we write J k,M (Γ) instead of J ρ,M (Γ) and call k the weight of the corresponding Jacobi forms. For more results about Jacobi forms with g > 1 and h > 1, we refer to [26,27,28,29,30,31,32] and [33]. Jacobi forms play an important role in lifting elliptic cusp forms to Siegel cusp forms of degree 2g (cf.…”

Section: Stable Jacobi Formsmentioning

confidence: 99%

Stable Schottky-Jacobi Forms

Yang

2017

Preprint

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Geometry and Arithmetic on the Siegel–Jacobi Space

Abstract: Furthermore M 1 and M 2 are differential operators on H n,m invariant under the action (1.2) of G J .

Cited by 7 publications

References 63 publications

A Hall of Statistical Mirrors

A Hall of Statistical Mirrors

Problems in the Geometry of the Siegel-Jacobi Space

Stable Schottky-Jacobi Forms

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