Tamagawa Numbers
For more general G, the Tamagawa number is defined (or indirectly computed) as the measure of
- G(A)/G(K).
Tsuneo Tamagawa's observation was that, starting from an invariant differential form ω on G, defined over K, the measure involved was well-defined: while ω could be replaced by cω with c a non-zero element of K, the product formula for valuations in K is reflected by the independence from c of the measure of the quotient, for the product measure constructed from ω on each effective factor. The computation of Tamagawa numbers for semisimple groups contains important parts of classical quadratic form theory.
Read more about this topic: Adelic Algebraic Group
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