On certain combination of colored multizeta values

Abstract

We reduce the sum ${\sum }_{k=1}^{\infty }{\sum }_{j=0}^{k-1}\frac{(-1{)}^{j+k+1}}{(2j+1{)}^{m}k}$ in terms of special values of the Dirichlet L-series in the character of conductor 4. This sum is a combination of colored zeta values.

References in corpus (2)

• Some examples of Mahler measures as multiple polylogarithms
• Mahler measure of some n-variable polynomial families

Cited by in corpus (1)

• Mahler measures and computations with regulators