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Computations in weight 3 of higher Bloch groups
Abstract
We computationally investigate a weight 3 analogue of the relationship between higher Bloch groups, algebraic K-theory, higher regulators, and special values of Dedekind zeta functions. In particular, for F a number field F, we define the pruned Bloch group B _3(F) and compare the covolume of its regulator lattice with zeta_F(3). We define a quantity kappa_3(F), which is conjecturally an integer, that is expected to be closely related to the order of K_4(O_F).
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BibTeX
@misc{gangl2026computations,
title = {{Computations in weight 3 of higher Bloch groups}},
author = {Herbert Gangl and Paul E. Gunnells and Dan Yasaki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36136},
eprint = {2610.36136},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36136},
}
RIS
TY - UNPB
TI - Computations in weight 3 of higher Bloch groups
AU - Herbert Gangl
AU - Paul E. Gunnells
AU - Dan Yasaki
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36136
UR - https://arxiv.org/abs/2610.36136
AB - We computationally investigate a weight 3 analogue of the relationship between higher Bloch groups, algebraic K-theory, higher regulators, and special values of Dedekind zeta functions. In particular, for F a number field F, we define the pruned Bloch group B _3(F) and compare the covolume of its regulator lattice with zeta_F(3). We define a quantity kappa_3(F), which is conjecturally an integer, that is expected to be closely related to the order of K_4(O_F).
ER -