Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On Carlitz’s Type q-Euler Numbers Associated with the Fermionic P -Adic Integral on Zp | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 358986 13 pages doi 2010 358986 Research Article On Carlitz s Type q-Euler Numbers Associated with the Fermionic P-Adic Integral on Zp Min-Soo Kim 1 Taekyun Kim 2 and Cheon-Seoung Ryoo3 1 Department of Mathematics Korea Advanced Institute of Science and Technology 373-1 Guseong-dong Yuseong-Gu Daejeon 305-701 Republic of Korea 2 Division of General Education-Mathematics Kwangwoon University Seoul 139-701 Republic of Korea 3 Department of Mathematics Hannam University Daejeon 306-791 Republic of Korea Correspondence should be addressed to Taekyun Kim tkkim@ Received 2 August 2010 Accepted 28 September 2010 Academic Editor Jewgeni Dshalalow Copyright 2010 Min-Soo Kim et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We consider the following problem in the paper of Kim et al. 2010 Find Witt s formula for Carlitz s type q-Euler numbers. We give Witt s formula for Carlitz s type q-Euler numbers which is an answer to the above problem. Moreover we obtain a new p-adic ợ-l-function lp q s x for Dirichlet s character X with the property that lp q -n x En xn q - n y p nEnXnqp for n 0 1 . using the fermionic p-adic integral on Zp . 1. Introduction Throughout this paper let p be an odd prime number. The symbol Zp Qp and Cp denote the rings of p-adic integers the field of p-adic numbers and the field of p-adic completion of the algebraic closure of Qp respectively. The p-adic absolute value in Cp is normalized in such way that p p p-1. Let N be the set of natural numbers and Z N u 0 . As the definition of q-number we use the following notations x q 1 - qx Ĩ-Ĩ x -q 1 - - x 1 q Note that limq 1 x q x for x e Zp where q tends to 1 in the region 0 q - 1 p 1. When one talks of q-analogue q is variously .
