## Journal of the Mathematical Society of Japan

- J. Math. Soc. Japan
- Volume 55, Number 4 (2003), 1061-1080.

### Fundamental Hermite constants of linear algebraic groups

#### Abstract

Let $G$ be a connected reductive algebraic group defined over a global field $k$ and $Q$ a maximal $k$-parabolic subgroup of $G$. The constant $\gamma (G,Q,k)$ attached to $(G,Q)$ is defined as an analogue of Hermite's constant. This constant depends only on $G,$$Q$ and $k$ in contrast to the previous definition of generalized Hermite constants ([**W1**]). Some functorial properties of $\gamma (G,Q,k)$ are proved. In the case that $k$ is a function field of one variable over a finite field, $\gamma (G{L}_{n},Q,k)$ is computed.

#### Article information

**Source**

J. Math. Soc. Japan, Volume 55, Number 4 (2003), 1061-1080.

**Dates**

First available in Project Euclid: 3 October 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.jmsj/1191418764

**Digital Object Identifier**

doi:10.2969/jmsj/1191418764

**Mathematical Reviews number (MathSciNet)**

MR2003760

**Zentralblatt MATH identifier**

1103.11033

**Subjects**

Primary: 11R56: Adèle rings and groups

Secondary: 11G35: Varieties over global fields [See also 14G25] 14G25: Global ground fields

**Keywords**

Hermite constant Tamagawa number linear algebraic group

#### Citation

WATANABE, Takao. Fundamental Hermite constants of linear algebraic groups. J. Math. Soc. Japan 55 (2003), no. 4, 1061--1080. doi:10.2969/jmsj/1191418764. https://projecteuclid.org/euclid.jmsj/1191418764