# The Bloch groups and special values of Dedekind zeta functions

## TL;DR

This paper compares definitions of Bloch groups, surveys their elements, and confirms the Lichtenbaum conjecture for certain fields, providing new insights into special zeta values and algebraic K-theory structures.

## Contribution

It introduces a comparison of Bloch group definitions, confirms the Lichtenbaum conjecture for specific fields, and explores zeta values and tame kernels using computational methods.

## Key findings

- Confirmed Lichtenbaum conjecture for $Q(\
- Derived equations for zeta functions at special values
- Analyzed the structure of tame kernels in various fields

## Abstract

In this paper, we compare the two definitions of Bloch group, and survey the elements in Bloch group. We confirm the Lichtenbaum conjecture on the field $Q(\zeta_p)$ under the assumption the truth of the base of the Bloch group of $Q(\zeta_p)$ and the relations of $K_2$ group. We also study the Lichtenbaum conjecture on non-Galois fields. By PARI, we get some equations of the zeta functions on special values and the structure of tame kernel of these fields.