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Constructing Modular Forms from Harmonic Maass Jacobi Forms
We construct a family of modular forms from harmonic Maass Jacobi forms by considering their Taylor expansion and using the method of holomorphic...
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Trace identities for the topological vertex
The topological vertex is a universal series which can be regarded as an object in combinatorics, representation theory, geometry, or physics. It...
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Quantum Jacobi forms and finite evaluations of unimodal rank generating functions
In this paper, we introduce the notion of a quantum Jacobi form, and offer the two-variable combinatorial generating function for ranks of strongly...
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Differential operators for Siegel-Jacobi forms
For any positive integers n and m , H n , m := H n ×C ( m , n ) is called the Siegel-Jacobi space, with the Jacobi group acting on it. The Jacobi forms are...
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Negative index Jacobi forms and quantum modular forms
In this paper, we consider the Fourier coefficients of a special class of meromorphic Jacobi forms of negative index considered by Kac and Wakimoto....
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Umbral moonshine and the Niemeier lattices
In this paper, we relate umbral moonshine to the Niemeier lattices - the 23 even unimodular positive-definite lattices of rank 24 with non-trivial...
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A note on Fourier-Jacobi coefficients of Siegel modular forms
Let F be a Siegel cusp form of weight k and genus n > 1 with Fourier-Jacobi coefficients f m . In this article, we estimate the growth of the...
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Siegel cusp forms of degree 2 are determined by their fundamental Fourier coefficients
We prove that a Siegel cusp form of degree 2 for the full modular group is determined by its set of Fourier coefficients a ( S ) with 4 det( S ) ranging...
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Fourier-Jacobi expansion and the Ikeda lift
In this article, we consider a Fourier-Jacobi expansion of Siegel modular forms generated by the Ikeda lift. There are two purposes of this article:...
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Eichler integrals, period relations and Jacobi forms
This paper contains three main results: the first one is to derive two “period relations” and the second one is a complete characterization of period...
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On the analogue of Weil’s converse theorem for Jacobi forms and their lift to half-integral weight modular forms
We generalize Weil’s converse theorem to Jacobi cusp forms of weight k , index m and Dirichlet character χ over the group Γ 0 ( N )⋉ℤ 2 . Then two...
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A Jacobi-Eisenstein series of weight two on congruence Jacobi subgroup
The specific aims of this paper are to define a Jacobi-Eisenstein series of weight two on congruence Jacobi subgroup and to compute its Fourier...
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Some aspects of Hermitian Jacobi forms
We introduce a certain differential (heat) operator on the space of Hermitian Jacobi forms of degree 1, show its commutation with certain Hecke...
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Construction of Jacobi forms associated to indefinite quadratic forms
Vignéras constructs non-holomorphic theta functions according to indefinite quadratic forms with arbitrary signature. We use Vignéras’ theta...
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A remark on a paper of Ibukiyama and Skoruppa
It was proved by Ibukiyama and Skoruppa that the spaces J 1, m ( l ) of Jacobi forms of weight 1, index m and level l vanish if gcd ( l , m )=1. We will...
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On dimension formulas for Jacobi forms
In this paper, we discuss the dimension formula for Jacobi forms via the Selberg trace formula, an explicit dimension formula for the space of Jacobi...