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Barnes-type degenerate Bernoulli polynomials
김대산,T. Kim,D. V. Dolgy,T KOMATSU 장전수학회 2015 Advanced Studies in Contemporary Mathematics Vol.25 No.1
In this paper, for any positive integer r, we consider the Barnes-type degenerate Bernoulli polynomials βn(λ, x|a1,...,ar) (a1,...,ar ≠ 0), generalizing the degener- ate Bernoulli polynomials βn(λ, x) (λ ≠ 0). From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities.
Sheffer sequences for the powers of Sheffer pairs under umbral composition
김대산,T. Kim,C. S. Ryoo 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.2
In this paper we study some properties of Sheffer sequences for the powers of Sheffer pairs under umbral composition.
Symmetry identities for generalized twisted Euler polynomials twisted by unramified roots of unity
김대산 장전수학회 2012 Proceedings of the Jangjeon mathematical society Vol.15 No.3
We derive three identities of symmetry in two variables and eight in three variables related to generalized twisted Euler polynomials and alternating generalized twisted power sums, both of which are twisted by unramified roots of unity. The case of ramified roots of unity was treated previously. The derivations of identities are based on the p-adic integral expression, with respect to a measure similar to that introduced by Koblitz, of the generating function for the generalized twisted Euler polynomials and the quotient of p-adic integrals that can be expressed as the exponential generating function for the alternating generalized twisted power sums.
A note on q-Eulerian polynomials
김대산,김태균 장전수학회 2013 Proceedings of the Jangjeon mathematical society Vol.16 No.4
In this paper, we consider a new construction of the q-extension of Eulerian polynomials which are different from Carlits's q-Eulerian polynomials
ON THE ASSOCIATED SEQUENCE OF SPECIAL POLYNOMIALS
김대산,김태균,이승훈,임석훈 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.2
In this paper, we investigate some properties of the associated sequence of Daehee and Changhee polynomials. Finally, we give some interesting identities of associated sequence involving some special polynomials.
Abundant symmetry for higher-order Bernoulli polynomials (II)
김대산,이나리,JIYOUNG NA,박경호 장전수학회 2013 Proceedings of the Jangjeon mathematical society Vol.16 No.3
We derive twenty five basic identities of symmetry in three vari-ables related to higher-order Bernoulli polynomials and power sums. Thisdemonstrates that there are abundant identities of symmetry in the threevariable case, in contrast to the two variable case, where there are only a few. These are new, since there have been results only about identities of symmetryin two variables. The derivations of identities are based on the p-adic integralexpression of the generating function for the higher-order Bernoulli polyno-mials and the quotient of integrals that can be expressed as the exponentialgenerating function for the power sums.
Codes associated with O(3,2^r) and power moments of Kloosterman sums with trace one arguments
김대산 장전수학회 2012 Proceedings of the Jangjeon mathematical society Vol.15 No.2
We construct a binary linear code C(O(3; q)), associated with the orthogonal group O(3; q). Here q is a power of two. Then we obtain a recursive formula for the odd power moments of Kloosterman sums with trace one arguments in terms of the frequencies of weights in the codes C(O(3; q)) and C(Sp(2; q)). This is done via Pless power moment identity and by utilizing the explicit expressions of Gauss sums for the orthogonal groups.
Some arithmetic properties of Bernoulli and Euler numbers
김대산,T. Kim,김영희,S. H. LEE 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.4
In this paper, we give some arithmatic identities for the Bernoulli and the Euler numbers. These identities are derived from the several p-adic integral equations on Z_p.
Some identities of Bernoulli and Euler polynomials arising form umbral calculus
김대산,김태균 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.1
In this paper, we give some interesting identities of Bernoulli and Euler polynomials which are derived from umbral calculus.
김대산 서울여자대학교 자연과학연구소 1990 자연과학연구논문집 Vol.1 No.-
F=F_(q)가 유한체이고, χ가 F의 곱지표, λ가 F의 자명하지 않은 합지표라고 하자. 이때 G₁(χ, λ)=∑□χ(u)λ(u)가 통상적인 가우스 합이고, G_(n)(χ, λ)=1/q□∑□χοdet(u)λοtr(u)가 지료들을 일반선형군으로 끌어올림으로써 얻어진 새로운 가우스 합이라고 할 때 G_(n)(χ, λ)=G₁(χ, λ)^(n)이 성립함을 보였다. 이 항등식은 고전적인 Davenport-Hasse 정리와 유사하며 이것은 일반선형군의 분해공식을 유도하여 바닥 최대포물부분군만이 합에 기여한다는 것을 이용하여 밝힐 수 있다.