q-Euler and Genocchi numbers

2005/06/14 by Taekyun Kim, Kim, Taekyun
Mathematics · #11B68 #11S80 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B68 #msc:11S80

paper · pdf · doi:10.48550/arxiv.math/0506278

7 pages

arxiv created 2005/06/14 · arxiv updated 2009/12/01

Abstract

Carlitz has introduced an interesting q-analogue of Frobenius-Euler numbers in [4]. He has indicated a corresponding Stadudt-Clausen theorem and also some interesting congruence properties of the q-Euler numbers. In this paper we give another construction of q-Euler numbers, which are different than his q-Euler numbers. By using our q-Euler numbers, we define the q-analogue of Genocchi numbers and investigate the relations between q-Euler numbers and q-analogs of Genocchi numbers.

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