• 대한전자공학회논문지
• /
• 제15권5호
• /
• pp.29-33
• /
• 1978

본 논문에서는 Galois 스윗칭함수를 구하기 위해서 임의의 유한체상에서 정의되는 Galois 체의 성질을 설명하였고, 임의의 유한체상에서의 연산방법을 밝혔다. 고리고 Lagrange 보간법에 의한 다항식이 유한체상에서 전개될 수 있음을 증명하였다 이 결과를 적용하여 단일변수를 갖는 Galois스윗칭 함수를 유도하고 다치논리회로를 실현하였다.

• Kyungpook Mathematical Journal
• /
• 제48권2호
• /
• pp.323-330
• /
• 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
• /
• 제56권4호
• /
• pp.1135-1140
• /
• 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
• /
• 제17권1호
• /
• pp.43-52
• /
• 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].

• 대한수학회보
• /
• 제58권3호
• /
• pp.617-635
• /
• 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.

• 충청수학회지
• /
• 제22권4호
• /
• pp.799-814
• /
• 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).

• 충청수학회지
• /
• 제26권1호
• /
• pp.213-219
• /
• 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 $D{\equiv}64(mod72)$.

• 충청수학회지
• /
• 제24권4호
• /
• pp.921-925
• /
• 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).

• 충청수학회지
• /
• 제23권4호
• /
• pp.853-860
• /
• 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).

• 충청수학회지
• /
• 제27권2호
• /
• pp.205-210
• /
• 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.