ABSTRACT
Tamagawa number Suppose that F is an algebraic number field of finite degree and G is a connected algebraic group defined over F . Denote by GF the group of all F -rational points on G, by GA the adele group of A, by I the idele group of G, by M the module of all F -rational characters of G, and by | · | the standard norm in I . Denote by G0A the set of all elements of GA such that |χA(g)| = 1 for each element χ of M . The volume of G0A/GF with respect to the normalized invariant measure is called the Tamagawa number of G.
