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

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Theorem5.Letk∈N.Thenthereexists

Lq,E( k,χ)=Ek,χ,q.

LetaandFbeintegerswith0<a<F.Fors∈C,weconsiderthefunctionsHq(s,a,F)asfollows:

Hq,E(s,a,F)=[2]q

qms( 1)m

[2]qF

saa[F] q( 1)qζqF(s,

( k,1)

a

m≡a(F),m>0

[2]qF

( n,1)

[F]nEqn,qF(

a