• Kyungpook Mathematical Journal
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• 제53권1호
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• pp.49-86
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• 2013

This article is a continuation of the paper [21]. In this paper we deal with Maass-Jacobi forms on the Siegel-Jacobi space $\mathbb{H}{\times}\mathbb{C}^m$, where H denotes the Poincar$\acute{e}$ upper half plane and $m$ is any positive integer.

• 대한수학회보
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• 제57권2호
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• pp.481-488
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• 2020

In this paper we give an exact formula for the Fourier coefficients of the Jacobi-Eisenstein series of square free discriminant lattice index. For a special case the discriminant of lattice is prime we show that the Jacobi-Eisenstein series corresponds to a well known Eisenstein series of modular forms.

• Kyungpook Mathematical Journal
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• 제43권4호
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• pp.547-566
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• 2003

In this paper, we introduce the notion of Maass-Jacobi forms and investigate some properties of these new automorphic forms. We also characterize these automorphic forms in several ways.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.993-1002
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• 2016

In this paper we give some non-existence theorems for parallel normal Jacobi operator of real hypersurfaces in real, complex and quaternionic space forms, respectively.

• Kyungpook Mathematical Journal
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• 제63권4호
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• pp.647-707
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• 2023

In this article, we discuss and survey the recent progress towards the Schottky problem, and make some comments on the relations between the André-Oort conjecture, Okounkov convex bodies, Coleman's conjecture, stable modular forms, Siegel-Jacobi spaces, stable Jacobi forms and the Schottky problem.

• 대한수학회보
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• 제50권2호
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• pp.559-581
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• 2013

This paper is motivated by a 2001 paper of Choie and Kim and a 2006 paper of Bump and Choie. The paper of Choie and Kim extends an earlier result of Bol for elliptic modular forms to the setting of Siegel and Jacobi forms. The paper of Bump and Choie provides a representation theoretic interpretation of the phenomenon, and shows how a natural generalization of Choie and Kim's result on Siegel modular forms follows from a natural conjecture regarding ($g$, K)-modules. In this paper, it is shown that the conjecture of Bump and Choie follows from work of Boe. A second proof which is along the lines of the proof given by Bump and Choie in the genus 2 case is also included, as is a similar treatment of the result of Choie and Kim on Jacobi forms.

• 대한수학회논문집
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• 제12권2호
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• pp.373-382
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• 1997

When the target manifold is a Sasakian or cosympletic space form, we characterize invariant immersions, tangential anti-invariant immersions and normal anti-invariant immersions by the spectra of the Jacobi operator.

• 대한수학회보
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• 제50권6호
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• pp.2089-2101
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• 2013

The aim of this paper is to introduce the notion of Lie recurrent structure Jacobi operator for real hypersurfaces in non-flat complex space forms and to study such real hypersurfaces. More precisely, the non-existence of such real hypersurfaces is proved.

• East Asian mathematical journal
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• 제17권1호
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• pp.103-114
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• 2001

When the target manifold is certain Kenmotsu manifolds, we characterize invariant immersions, tangential anti-invariant immersions and normal anti-invariant immersions by the spectra of the Jacobi operator.

• 대한수학회지
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• 제53권3호
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• pp.645-689
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• 2016

This article gives upper bounds on the number of Fourier-Jacobi coefficients that determine a paramodular cusp form in degree two. The level N of the paramodular group is completely general throughout. Additionally, spaces of Jacobi cusp forms are spanned by using the theory of theta blocks due to Gritsenko, Skoruppa and Zagier. We combine these two techniques to rigorously compute spaces of paramodular cusp forms and to verify the Paramodular Conjecture of Brumer and Kramer in many cases of low level. The proofs rely on a detailed description of the zero dimensional cusps for the subgroup of integral elements in each paramodular group.