• Journal of the Korean Institute of Telematics and Electronics
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• v.15 no.5
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• pp.29-33
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• 1978

In this paper, the properties of Galois fields defined over any finite field are analysed to derive Galois switching functions and the arithmetic operation methods over any finite field are showed. The polynomial expansions over finite fields by Lagrange's interpolation method are derived and proved. The results are applied to multivalued single variable logic networks.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.323-330
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• 2008

Some finiteness and non-existence results are proved of 2-dimensional mod 2 Galois representations of quadratic fields unramified outside 2.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1135-1140
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• 2016

Let A be an abelian variety over a global field K. We know [6, 7] that, in many cases, the average number of n-torsion points of A over various residue fields of K, takes the minimal possible value. In this article, we study several defect cases by calculating the number of Galois orbits.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.43-52
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• 2009

The Galois ring is a finite extension of the ring of integers modulo a prime power. We consider characters on Galois rings. In analogy with finite fields, we investigate complete Gauss sums over Galois rings. In particular, we analyze [1, Proposition 3] and give some lemmas related to [1, Proposition 3].

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.617-635
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• 2021

Let X be a smooth hypersurface X of degree d ≥ 4 in a projective space ℙⁿ⁺¹. We consider a projection of X from p ∈ ℙⁿ⁺¹ to a plane H ≅ ℙⁿ. This projection induces an extension of function fields ℂ(X)/ℂ(ℙⁿ). The point p is called a Galois point if the extension is Galois. In this paper, we will give necessary and sufficient conditions for X to have Galois points by using linear automorphisms.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.799-814
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• 2009

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of some class invariants from the generalized Weber functions $\mathfrak{g}_0,\mathfrak{g}_1,\mathfrak{g}_2$ and $\mathfrak{g}_3$ over quadratic number fields with discriminant $D{\equiv}1$ (mod 12).

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.213-219
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• 2013

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, we compute the Galois actions of a class invariant from a generalized Weber function $g_1$ over imaginary quadratic number fields with discriminant $D{\equiv}64(mod72)$.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.921-925
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• 2011

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}21$ (mod 36).

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.853-860
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• 2010

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}-3$ (mod 36).

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.205-210
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• 2014

The author with C. H. Kim and Y. Lee constructed infinite families of elliptic curves over cubic number fields K with prescribed torsion groups which occur infinitely often. In this paper, we examine the Galois structures of such cubic number fields K for the families of elliptic curves with cyclic torsion.