Journal of the
Korean Mathematical Society JKMS

The main result of this paper is to construct the derivative twisted $p$-adic $(h,q)$-$L$-functions at $s=0$. We obtain twisted version of Theorem 4 in [17]. We also obtain twisted $(h,q)$-extension of Proposition 1 in [3].

Keywords: $q$-Bernoulli numbers and polynomials, twisted $q$-Bernoulli numbers and polynomials, $q$-zeta function, $p$-adic $L$-function, twisted $q$-zeta function, twisted $q$-$L$-functions, $q$-Volkenborn integral.

MSC numbers: 11B68, 11S40, 11S80, 11B99, 28B99