The aim of this paper is to construct new Dedekind type sums. We construct generating functions of Barnes’ type multiple FrobeniusEuler numbers and polynomials. By applying Mellin transformation to these functions, we define Barnes’ type multiple l-functions, which interpolate Frobenius-Euler numbers at negative integers. By using generalizations of the Frobenius-Euler functions, we define gene...

Let p be a fixed prime. Throughout this paper Zp, Qp, C and Cp will, respectively, denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field and the completion of algebraic closure of Qp, cf.[1, 4, 6, 10]. Let vp be the normalized exponential valuation of Cp with |p|p = p −vp(p) = p. When one talks of q-extension, q is variously considered as an...

Abstract. The main purpose of this paper is to prove an identity of symmetry for the Frobenius-Euler polynomials. It turns out that the recurrence relation and multiplication theorem for the Frobenius-Euler polynomials which discussed in [ K. Shiratani, S. Yamamoto, On a p-adic interpolation function for the Euler numbers and its derivatives, Memo. Fac. Sci. Kyushu University Ser.A, 39(1985), 1...

Let p be a fixed odd positive integer. Throughout this paper Zp, Qp, C and Cp are respectively denoted as the ring of p-adic rational integers, the field of p-adic rational numbers, the complex numbers field and the completion of algebraic closure of Qp. The p-adic absolute value in Cp is normalized so that |p|p = 1/p. When one talks of q-extension, q is considered in many ways such as an indet...

‎hensel [k‎. ‎hensel‎, ‎deutsch‎. ‎math‎. ‎verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎then $|x...

Throughout this paper Z,Zp,Qp and Cp will be denoted by the ring of rational integers, the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp, respectively, cf. [7, 8, 9, 10]. Let νp be the normalized exponential valuation of Cp with |p|p = p −νp(p) = p. When one talks of qextension, q is variously considered as an indeterminate, a comple...

Let p be a fixed prime number. Throughout this paper, the symbols Z,Zp,Qp,C, and Cp will denote the ring of rational integers, the ring of p-adic integers, the field of p-adic rational numbers, the complex number field, and the completion of the algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z N ∪ {0}. Let vp be the normalized exponential valuation of Cp with |p|...