Professor Herbert Gangl's Outputs (29)

Multiple logarithms, algebraic cycles and trees (2007)
Book Chapter
Gangl, H., Goncharov, A. B., & Levin, A. (2007). Multiple logarithms, algebraic cycles and trees. In P. Cartier, P. Moussa, B. Julia, & P. Vanhove (Eds.), Frontiers in Number Theory, Physics, and Geometry II: On Conformal Field Theories, Discrete Groups and Renormalization (759-774). Springer. https://doi.org/10.1007/978-3-540-30308-4_16

This is a short exposition-mostly by way of the toy models double logarithm and triple logarithm-which should serve as an introduction to the article [3] in which we establish a connection between multiple polylogarithms, rooted trees and algebraic c... Read More about Multiple logarithms, algebraic cycles and trees.

Goncharov's trilogarithm relation on pictures. (2007)
Journal Article
Gangl, H. (2007). Goncharov's trilogarithm relation on pictures. Journal of Number Theory, 124(1), 17-25. https://doi.org/10.1016/j.jnt.2006.05.021

Double zeta values and modular forms (2006)
Presentation / Conference Contribution
Gangl, H., Kaneko, M., & Zagier, D. (2006, January). Double zeta values and modular forms. Presented at Automorphic forms and zeta functions, Tokyo, Japan

We give new relations among double zeta values and show that the structure of the Q-vector space of all (known) relations among double zeta values of weight k is connected in many different ways with the structure of the space of modular forms of wei... Read More about Double zeta values and modular forms.

Generators and Relations for K_2 O_F (2004)
Journal Article
Belabas, K., & Gangl, H. (2004). Generators and Relations for K_2 O_F. K-Theory, 31(3), 195 - 231. https://doi.org/10.1023/b%3Akthe.0000028979.91416.00

Tate's algorithm for computing K_2 O_F for rings of integers in a number field has been adapted for the computer and gives explicit generators for the group and sharp bounds on their order---the latter, together with some structural results on the p-... Read More about Generators and Relations for K_2 O_F.

Functional equations for higher logarithms (2003)
Journal Article
Gangl, H. (2003). Functional equations for higher logarithms. Selecta Mathematica (New Series), 9(3), 361 - 377. https://doi.org/10.1007/s00029-003-0312-z

Following earlier work by Abel and others, Kummer gave in 1840 functional equations for the polylogarithm function Li_m(z) up to m = 5, but no example for larger m was known until recently. We give the first genuine 2-variable functional equation for... Read More about Functional equations for higher logarithms.

Quelques calculs de la cohomologie de GL_N(Z) et de la K-theorie de Z (2002)
Journal Article
Elbaz-Vincent, P., Gangl, H., & Soulé, C. (2002). Quelques calculs de la cohomologie de GL_N(Z) et de la K-theorie de Z. Comptes Rendus Mathématique, 335(4), 321-324. https://doi.org/10.1016/s1631-073x%2802%2902481-0

Voronoi cell decomposition is used to determine most of the structure of the homology of GL_N(Z) for N=5, 6. This determines K_5(Z) and gives that K_6(Z) is a 3-group.

On poly(ana)logs I (2002)
Journal Article
Elbaz-Vincent, P., & Gangl, H. (2002). On poly(ana)logs I. Compositio Mathematica, 130(2), 161-214. https://doi.org/10.1023/a%3A1013757217319

We investigate a connection between the differential of polylogarithms (as considered by Cathelineau) and a finite variant of them. This allows to answer a question raised by Kontsevich concerning the construction of functional equations for the fini... Read More about On poly(ana)logs I.

Computing the tame kernel of quadratic imaginary fields (2000)
Journal Article
Browkin, J., Belabas, K., & Gangl, H. (2000). Computing the tame kernel of quadratic imaginary fields. Mathematics of Computation, 69(232), 1667-1683. https://doi.org/10.1090/s0025-5718-00-01182-0

J. Tate has determined the group K2script O signF (called the tame kernel) for six quadratic imaginary number fields F = ℚ(√d), where d = -3, -4, -7, -8,-11, -15. Modifying the method of Tate, H. Qin has done the same for d = -24 and d = -35, and M.... Read More about Computing the tame kernel of quadratic imaginary fields.

Tame and wild kernels of quadratic imaginary number fields (1999)
Journal Article
Browkin, J., & Gangl, H. (1999). Tame and wild kernels of quadratic imaginary number fields. Mathematics of Computation, 68(225), 291-305. https://doi.org/10.1090/s0025-5718-99-01000-5

For all quadratic imaginary number fields F of discriminant d > -5000, we give the conjectural value of the order of Milnor's group (the tame kernel) K2OF, where OF is the ring of integers of F. Assuming that the order is correct, we determine the st... Read More about Tame and wild kernels of quadratic imaginary number fields.