• Journal of the Korean Mathematical Society
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• 제61권1호
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• pp.65-90
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• 2024

In this paper, we introduce the notion of the stability of automorphic forms for the general linear group and relate the stability of automorphic forms to the moduli space of real tori and the Jacobian real locus.

• 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.

• Journal of the Korean Mathematical Society
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• 제40권5호
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• pp.831-867
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• 2003

In this paper, we find the unitary dual of the group SL(2,R)(equation omitted)R($^{m,2}$) and study automorphic forms related to the group SL(2,R)(equation omitted)R($^{m, 2}$).).

• Kyungpook Mathematical Journal
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• 제14권1호
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• pp.55-61
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• 1974

• Korean Journal of Mathematics
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• 제3권1호
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• pp.1-4
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• 1995

• Kyungpook Mathematical Journal
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• 제14권1호
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• pp.1-6
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• 1974

• Journal of the Korean Mathematical Society
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• 제50권2호
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• pp.275-306
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• 2013

For two positive integers $m$ and $n$, let $\mathcal{P}_n$ be the open convex cone in $\mathbb{R}^{n(n+1)/2}$ consisting of positive definite $n{\times}n$ real symmetric matrices and let $\mathbb{R}^{(m,n)}$ be the set of all $m{\times}n$ real matrices. In this paper, we investigate differential operators on the non-reductive homogeneous space $\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}$ that are invariant under the natural action of the semidirect product group $GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}$ on the Minkowski-Euclid space $\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}$. These invariant differential operators play an important role in the theory of automorphic forms on $GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}$ generalizing that of automorphic forms on $GL(n,\mathbb{R})$.

• Kyungpook Mathematical Journal
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• 제45권3호
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• pp.303-338
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• 2005

In this paper, we study unitary representations of the group $GL(n,{\mathbb{R}}){\ltimes}{\mathbb{R}}^{(m,n)}$.

• Communications of the Korean Mathematical Society
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• 제38권2호
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• pp.319-330
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• 2023

In this paper, we obtain certain estimates for averages of shifted convolution sums involving Hecke eigenvalues of classical holomorphic cusp forms. This generalizes some results of Lü and Wang in this direction.

• Bulletin of the Korean Mathematical Society
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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.