Evaluations of a class of double 𝐿-values

Abstract

Abstract. An analytic proof of an evaluation theorem for the "convolution"-type double L-values of non-principal characters is given. Along the way, Dirichlet character analogues of generalized single and double polylogarithms are defined. The monodromies of these functions play a pivotal role.

Functional Equations for Double L-Functions and Values at Non-Positive Integers

“…After their work, several properties for MLVs have been studied (see, for example, [25,26,28]). In addition, another type of multiple L-functions was studied by Akiyama and Ishikawa [2,13].…”

Evaluation of one-dimensional polylogarithmic integral, with applications to infinite series

“…Denote the Q-span of weight n and level N CMZVs by CMZV N n . There have been a lot of researches on Q-dimensions spanned by CMZV ( [1], [30], [36], [37], [41], [40]). Let d(w, N ) be the dimension of CMZV N w , a deep result due to Deligne and Goncharov [23] provides an upper bound of d(w, N ): Theorem 1.1.…”