Abstract
We consider the following problem in the paper of Kim et al. (2010): Find Witt's formula for Carlitz's type -Euler numbers. We give Witt's formula for Carlitz's type -Euler numbers, which is an answer to the above problem. Moreover, we obtain a new p-adic q-l-function for Dirichlet's character , with the property that for using the fermionic p-adic integral on .
Highlights
Throughout this paper, let p be an odd prime number
We give Witt’s formula for Carlitz’s type q-Euler numbers, which is an answer to the above problem
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
Summary
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. We obtain a new p-adic q-l-function lp,q s, χ for Dirichlet’s character χ, with the property that lp,q −n, χ. Using the fermionic p-adic integral on Zp
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