A STUDY ON THE TWISTED q-EULER POLYNOMIALS ... - CiteSeerX
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A STUDY ON THE TWISTED q-EULER POLYNOMIALS ... - CiteSeerX
Received February 19, 2011. Revised June 8, 2011. Accepted August 22, 2011. âCorresponding author. â This work was supported by Konkuk University 2011.
J. Appl. Math. & Informatics Vol. 30(2012), No. 1 - 2, pp. 321 - 325
Website: http://www.kcam.biz
A STUDY ON THE TWISTED q-EULER POLYNOMIALS AND TRANSFER OPERATORS† LEE-CHAE JANG AND WONJOO KIM∗
Abstract. In this paper, we consider twisted q-Euler polynomials and define a p-adic q-transfer operator (see [6]). From this operator, we investigate the eigenvalues of the p-adic q-transfer operator on the space of twisted q-Euler polynomials. AMS Mathematics Subject Classification : 11B68, 11S80, 41A30. Key words and phrases : twisted q-Euler polynomials, p-adic q-integral, q-transfer operators.
1. Introduction Throughout this paper, Z, Q, Zp , Qp and Cp will denote the ring of rational integers, the field of rational numbers, the ring of p-adic integers, the field of padic rational numbers and the completion of algebraic closure of Qp , respectively. Let νp be the normalized exponential valuation of Cp such that |p |p = p−νp (p) = 1 p . Let q be regarded as either a complex number q ∈ C or a p-adic number q ∈ Cp . If q ∈ C, we assume |q| < 1, and if q ∈ Cp , we normally assume |1 − q|p < 1. We use the notation [x]q =
1 − qx 1−q
and [x]−q =
1 − (−q)x 1+q
for all x ∈ Zp . Let d be a fixed positive odd integer and let p be a fixed odd prime number. We now set X = Xd
