• 대한수학회지
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• 제44권1호
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• pp.11-24
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• 2007

The main purpose of this paper is to use the properties of primitive characters, Gauss sums and Ramanujan's sum to study the hybrid mean value of generalized Bernoulli numbers, general Kloosterman sums and Gauss sums, and give two asymptotic formulae.

• 대한수학회보
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• 제50권2호
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• pp.697-704
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• 2013

The function $g{\mapsto}{\zeta}^k_G(g)$ which counts the number of solutions of $x^k=g$ in a finite group G, is not necessarily a character of G. We study this function for the case of dihedral groups and generalized quaternion groups.

• 대한수학회지
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• 제32권4호
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• pp.689-695
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• 1995

Let G be a finite group with k distinct conjugacy classes $C_1, C_2, \cdots, C_k$ and F an algebraically closed field such that char$(F){\dag}\left$\mid$ G \right$\mid$$. We denoted by $Irr_F$(G) the set of all irreducible F-characters of G and $Cf_F$(G) the set of all class functions of G into F. Then $Cf_F$(G) is a commutative F-algebra with an F-basis $Irr_F(G) = {\chi_1, \chi_2, \cdots, \chi_k}$.

• 대한수학회보
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• 제20권2호
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• pp.87-93
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• 1983

Let X and Y be normed linear spaces. An operator T defined on X with the range in Y is continuous in the sense that if a sequence {x$_{n}$} in X converges to x for the weak topology .sigma.(X.X') then {Tx$_{n}$} converges to Tx for the norm topology in Y. We shall denote the class of such operators by WC(X, Y). For example, if T is a compact operator then T.mem.WC(X, Y). In this note we discuss relationships between WC(X, Y) and the class of weakly of bounded linear operators B(X, Y). In the last section, we will consider some characters for an operator in WC(X, Y).).

• 대한수학회논문집
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• 제29권4호
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• pp.497-503
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• 2014

In this paper, we consider characters of $SL_2(\mathbb{Z})$ and then apply them to newforms of integral weight, level 4 and of trivial character. More precisely, we prove that all of them are actually level 1 forms of some nontrivial character. As a byproduct, we prove that they all are eigenfunctions of the Fricke involution with eigenvalue -1.

• 대한수학회논문집
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• 제9권3호
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• pp.521-529
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• 1994

This paper studies the realization of irreducible unitary representations of $GL_2(R)$ and $GL_2(C)$ by Bargmann's classification[1]. Since the representations of general matrix groups can be obtained by the extensions of characters of a special linear group, we shall follow to a large extent the pattern of the results in [5], [6], and [8]. This article is divided into two sections. In the first section we describe the realization of principal series and discrete series and complementary series of $GL_2(R)$. The last section is devoted to the derivation of principal series and complementary series of $GL_2(C).

• 대한수학회지
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• 제57권3호
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• pp.571-583
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• 2020

The Galois ring R of characteristic pⁿ having p^mn elements is a finite extension of the ring of integers modulo pⁿ, where p is a prime number and n, m are positive integers. In this paper, we develop the concepts of Jacobi sums over R and under the assumption that the generating additive character of R is trivial on maximal ideal of R, we obtain the basic relationship between Gauss sums and Jacobi sums, which allows us to determine the absolute value of the Jacobi sums.

• 대한수학회지
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• 제43권6호
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• pp.1199-1217
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• 2006

The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the T-th hyper-Kloosterman sums Kl(h, k+1, r;q) and the hyper Cochrane sums C(h, q; m, k), and give an interesting mean value formula.

• 충청수학회지
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• 제35권1호
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• pp.1-12
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• 2022

In this paper we prove an even characteristic analogue of the result of Andrade on lower bounds for moment of quadratic Dirichlet L-functions in odd characteristic. We establish lower bounds for the moments of Dirichlet L-functions of characters defined by Hasse symbols in even characteristic.

• 한국게임학회 논문지
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• 제7권3호
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• pp.23-30
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• 2007

게임 밸런스는 게임 디자인의 매우 중요한 요소이며, 게임을 좀 더 재미있게 구성하기 위한 필수 요소이다. 대부분의 게임 개발사들은 성공적인 게임 개발을 위하여 자체적인 밸런스 방법을 사용한다. 효율적인 밸런스 방법이 항상 성공적인 게임 개발을 보장할 수는 없으나 게임 개발자의 입장에서 효율적인 게임 개발을 위하여 표준적인 밸런스 방법이 필요한 것이 사실이다. 캐릭터간의 전투 시스템은 주로 액션을 포함한 장르에서 구현된다. 캐릭터간의 전투를 위한 직접적인 밸런스 요소는 각 캐릭터들이 가지게 되는 특성 및 공격 형태들이다. 본 논문에서 우리는 캐릭터간의 대전 시스템을 갖는 게임에서 캐릭터와 관련된 직접적인 밸런스 요소를 구분하고 이에 근간한 수학적 밸런스 방법을 제안한다.