Introduction

Let K be a global field (for example, the field Q of rational numbers). To every connected semisimple algebraic group G over K, one can associate a locally compact group G(A), called the group of adelic points of G. The group G(A) comes equipped with a canonical left-invariant measure μ Tam, called Tamagawa measure, and a discrete subgroup G(K) ⊆ G(A). The Tamagawa measure of the quotient G(K)\G(A) is a nonzero real number τ(G), called the Tamagawa number of the group G. A celebrated conjecture of Weil asserts that if the algebraic group G is simply connected, then the Tamagawa number