A deformation of multiple L-values

In a previous paper, the first named author introduced a two-parameter deformation of multiple zeta values. Its generating function is given by a multiple integral whose integrand is a product of Kronecker’s double series. In this paper, we use a scaling limit of Kronecker’s double series to construct a one-parameter deformation of multiple L-values (dMLVs). We prove double shuffle relations among them and construct an entire function interpolating the dMLVs.