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On two conjectures of Sun concerning Apéry-like series (2023)
Journal Article
Charlton, S., Gangl, H., Lai, L., Xu, C., & Zhao, J. (2023). On two conjectures of Sun concerning Apéry-like series. Forum Mathematicum, 35(6), 1533-1547. https://doi.org/10.1515/forum-2022-0325

We prove two conjectural identities of Z.-W. Sun concerning Apéry-like series. One of the series is alternating, whereas the other one is not. Our main strategy is to convert the series and the alternating series to log-sine-cosine and log-sinh-cosh... Read More about On two conjectures of Sun concerning Apéry-like series.

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 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 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 for imaginary quadratic fields.

On the topological computation of K_4 of the Gaussian and Eisenstein integers (2018)
Journal Article
Gangl, H., Dutour Sikiriˇc, M., Gunnells, P., Hanke, J., Schuermann, A., & Yasaki, D. (2019). On the topological computation of K_4 of the Gaussian and Eisenstein integers. Journal of Homotopy and Related Structures, 14, 281-291. https://doi.org/10.1007/s40062-018-0212-8

In this paper we use topological tools to investigate the structure of the algebraic K-groups K4(R) for R=Z[i] and R=Z[ρ] where i:=−1−−−√ and ρ:=(1+−3−−−√)/2. We exploit the close connection between homology groups of GLn(R) for n≤5 and those of rela... Read More about On the topological computation of K_4 of the Gaussian and Eisenstein integers.

On the Broadhurst-Kreimer generating series for multiple zeta values (2015)
Book Chapter
Carr, S., Gangl, H., & Schneps, L. (2015). On the Broadhurst-Kreimer generating series for multiple zeta values. In L. Álvarez-Cónsul, J. Burgos Gil, & K. Ebrahimi-Fard (Eds.), Feynman amplitudes, periods, and motives : international research conference on periods and motives : a modern perspective on renormalization : July 2-6, 2012, Institute de Ciencias Matemáticas, Madrid, Spain (57-77). American Mathematical Society. https://doi.org/10.1090/conm/648/12998