In this paper we give the q-extension of Euler numbers which can be viewed as interpolating of the q-analogue of Euler zeta function ay negative integers, in the same way that Riemann zeta function interpolates Bernoulli numbers at negative integers. Final

8q-ANALOGUEOFRIEMANNZETAFUNCTION

8.T.Kim,q-BernoullinumbersandpolynomialsassociatedwithGaussianbinomialcoe cients,RussianJ.Math.Phys.15(2008),51-57.9.T.Kim,q-extensionoftheEulerformulaandtrigonometricfunctions,RussianJ.Math.Phys.14(2007),275-278.10.T.Kim,J.y.Choi,J.Y.Sug,Extendedq-Eulernumbersandpolynomialsassociatedwithfermionic

p-adicq-integralonZp,RussianJ.Math.Phys.14(2007),160-163.11.T.Kim,q-generalizedEulernumbersandpolynomials,RussianJ.Math.Phys.13(2006),293-298.12.T.Kim,Multiplep-adicL-function,RussianJ.Math.Phys.13(2006),151-157.

13.T.Kim,Powerseriesandasymptoticseriesassociatedwiththeq-analogofthetwo-variablep-adic

L-function,RussianJ.Math.Phys.12(2005),186-196.14.T.Kim,Analyticcontinuationofmultipleq-zetafunctionsandtheirvaluesatnegativeintegers,

RussianJ.Math.Phys.11(2004),71-76.15.T.Kim,OnEuler-Barnesmultiplezetafunctions,RussianJ.Math.Phys.10(2003),261-267.16.T.Kim,Themodi edq-Eulernumbersandpolynomials,Adv.Stud.Contemp.Math.16(2008),

161-170.17.T.Kim,Anoteonp-adicq-integralonZpassociatedwithq-Eulernumbers,Adv.Stud.Contemp.

Math.15(2007),133-137.18.T.Kim,Anoteonp-adicinvariantintegralintheringsofp-adicintegers,Adv.Stud.Contemp.

Math.13(2006),95-99.19.H.Ozden,Y.Simsek,S.-H.Rim,I.N.Cangul,Oninterpolationfunctionsofthetwistedgeneralized

Frobenius-Eulernumbers,Adv.Stud.Contemp.Math.15(2007),187-194.20.H.Ozden,Y.Simsek,I.N.Cangul,Multivariateinterpolationfunctionsofhigher-orderq-Euler

numbersandtheirapplications,AbstractandAppliedAnalysis2008(2008),Art.ID390857,16pages.21.H.Ozden,Y.Simsek,I.N.Cangul,Eulerpolynomialsassociatedwithp-adicq-Eulermeasure,

GeneralMathematics15(2007),24-37.22.Y.Simsek,GeneratingfunctionsofthetwistedBernoullinumbersandpolynomialsassociatedwith

theirinterpolationfunctions,Adv.Stud.Contemp.Math.16(2008),251-278.23.Y.Simsek,Y.Osman,V.Kurt,OninterpolationfunctionsofthetwistedgeneralizedFrobenius-Eulernumbers,Adv.Stud.Contemp.Math.15(2007),187-194.24.Y.Simsek,HardycharactersumsrelatedtoEisensteinseriesandthetafunctions,Adv.Stud.

Contemp.Math.12(2006),39-53.