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Professor Herbert Gangl's Outputs (29)

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 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.

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 cohomology of linear groups over imaginary quadratic fields (2016)
Journal Article
Dutour Sikirić, M., Gangl, H., Gunnells, P. E., Hanke, J., Schürmann, A., & Yasaki, D. (2016). On the cohomology of linear groups over imaginary quadratic fields. Journal of Pure and Applied Algebra, 220(7), 2564-2589. https://doi.org/10.1016/j.jpaa.2015.12.002

Let Γ be the group GLN(OD), where OD is the ring of integers in the imaginary quadratic field with discriminant D<0. In this paper we investigate the cohomology of Γ for N=3,4 and for a selection of discriminants: D≥−24 when N=3, and D=−3,−4 when N=4...

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

Tame kernels and second regulators of number fields and their subfields (2013)
Journal Article
Browkin, J., & Gangl, H. (2013). Tame kernels and second regulators of number fields and their subfields. K-Theory, 12(1), 137-165. https://doi.org/10.1017/is013005031jkt229

Assuming a version of the Lichtenbaum conjecture, we apply Brauer-Kuroda relations between the Dedekind zeta function of a number field and the zeta function of some of its subfields to prove formulas relating the order of the tame kernel of a number... Read More about Tame kernels and second regulators of number fields and their subfields.

Multiple polylogarithms, polygons, trees and algebraic cycles. (2009)
Book Chapter
Gangl, H., Goncharov, A., & Levin, A. (2009). Multiple polylogarithms, polygons, trees and algebraic cycles. In D. Abramovich, A. Bertram, L. Katzarkov, R. Pandharipande, & M. Thaddeus (Eds.), Algebraic geometry--Seattle 2005. Part 2 (547-593). American Mathematical Society

Multiple logarithms, trees and algebraic cycles (2007)
Book Chapter
Gangl, H., Goncharov, A., & Levin, A. (2007). Multiple logarithms, trees and algebraic cycles. In P. Cartier, B. Julia, P. Moussa, & P. Vanhove (Eds.), Frontiers in Number Theory, Physics and Geometry II (759-774). (New ed.). Springer Verlag

The differential properties of multiple logarithms and those of corresponding algebraic cycles are related to the combinatorics of certain trees.