Outputs (3)

On functional equations for Nielsen polylogarithms (2021)
Journal Article
Charlton, S., Gangl, H., & Radchenko, D. (2021). On functional equations for Nielsen polylogarithms. Communications in Number Theory and Physics, 15(2), 363-454. https://doi.org/10.4310/cntp.2021.v15.n2.a4

We derive new functional equations for Nielsen polylogarithms. We show that, when viewed moduloLi5 and products of lower weight functions, the weight 5 Nielsen polylogarithm S3,2 satisfies the dilogarithm five-term relation. We also give some functio... Read More about On functional equations for Nielsen polylogarithms.

Hyperbolic tessellations and generators of K₃ for imaginary quadratic fields (2021)
Journal Article
Burns, D., de Jeu, R., Gangl, H., Rahm, A. D., & Yasaki, D. (2021). Hyperbolic tessellations and generators of K₃ for imaginary quadratic fields. Forum of Mathematics, Sigma, 9, Article e40. https://doi.org/10.1017/fms.2021.9

We develop methods for constructing explicit generators, modulo torsion, of the K₃ -groups of imaginary quadratic number fields. These methods are based on either tessellations of hyperbolic 3 -space or on direct calculations in suitable pre-Bloch gr... Read More about Hyperbolic tessellations and generators of K₃ for imaginary quadratic fields.

Clean Single-Valued Polylogarithms (2021)
Journal Article
Charlton, S., Duhr, C., & Gangl, H. (2021). Clean Single-Valued Polylogarithms. Symmetry, integrability and geometry: methods and applications, 17, Article 107. https://doi.org/10.3842/SIGMA.2021.107

We define a variant of real-analytic polylogarithms that are single-valued and that satisfy “clean” functional relations that do not involve any products of lower weight functions. We discuss the basic properties of these functions and, for depths on... Read More about Clean Single-Valued Polylogarithms.