Motivic Artin \(L\)-functions and a motivic Tamagawa number (Q983424)

The author defines the motivic Artin \(L\)-fonctions via a motivic Euler product, and he shows that they coincide with the functions introduced by Dhillon and Minac. Under some assumptions he introduces the notion of the motivic Tamagawa number of a constant family and he showes that it specializes to the Tamagawa number introduced by Peyre in the context of Manin's conjectures about rational points of bounded height on Fano varieties.