• Honam Mathematical Journal
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• v.26 no.4
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• pp.365-378
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• 2004

The orders in quaternion algebras play central role in the theory of Hecke operators. In this paper, we study the order of two sided ideal group in orders of a quaternion algebra.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.297-304
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• 2012

There are several types of orders in a Quaternion algebra. Generally, zeta functions defined on orders of a Quaternion algebra give some informations on the ideal theory of orders. In this study, we investigate functional equalities between the zeta functions defined on orders of a Quaternion algebra.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.81-96
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• 2004

The level-m scaled circulant factor matrix over the complex number field is introduced. Its diagonalization and spectral decomposition and representation are discussed. An explicit formula for the entries of the inverse of a level-m scaled circulant factor matrix is presented. Finally, an algorithm for finding the inverse of such matrices over the quaternion division algebra is given.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.611-632
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• 2009

The orders in a quaternion algebra play a central role of the theory of Hecke operators. In this paper, we study the arithmetic properties of optimal embeddings of orders in a quaternion algebra over a dyadic local field.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.639-652
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• 2005

We find the class number of orders in a quaternion algebra over a dyadic local field.

• Honam Mathematical Journal
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• v.35 no.1
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• pp.73-82
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• 2013

There are some identities between the representations of Hecke operators defined on a subspace of modular forms associated with orders of a Quaternion algebra. In this paper, we find the identities between the zeta functions attached to these representations.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.343-358
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• 2008

The primitive orders in a quaternion algebra play a central role of the theory of Hecke operators. In this paper, we study theta series generated by Brandt matrices and its applications to almost Ramanujan graphs.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.231-238
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• 2005

In this paper, we study the arithmetic properties of orders in a quaternion algebra over a dyadic local field and we find the mass formula of orders.

• ETRI Journal
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• v.43 no.6
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• pp.978-990
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• 2021

This article presents techniques for improved estimation of symbol timing offset (STO) and carrier frequency offset (CFO) for dual-polarization (DP) orthogonal frequency division multiplex (DP-OFDM) systems. Recently, quaternion multiple-input multiple-output OFDM has been proposed for high spectral efficiency communication systems, which can flexibly explore different types of diversities such as space, time, frequency, and polarization. This article focuses on synchronization techniques for DP-OFDM systems using a cyclic prefix, where the application of quaternion algebra leads to new improved estimators. Simulations performed for DP system methods show faster reduction of STO estimator variance with a double-slope line in the logvariance line versus signal-to-noise ratio (SNR) plot compared with singlepolarization (SP) counterparts, and simulations for CFO estimates show a 3-dB gain of DP over SP estimates for same SNR values defined, respectively, for quaternion-valued or complex-valued signals. Cramer-Rao bounds for STO and CFO are derived for the synchronization methods, correlating with the observed gains of DP over SP OFDM systems.