On the motive of a reductive group
Following Steinberg, a motive \(M\) of Artin-Tate type is attached to any connected reductive group \(G\) over a field \(k.\) When \(k\) is a local field of characteristic 0, the \(L\)-function \(L(M)\) is finite if and only if Serre's Euler-Poincaré measure of \(G(k)\) is non-zero. In this case, a local function equation is obtained. When \(k\) is a number field, \(L(M)\) is used to evaluate certain adélic integrals in the trace formula.
scientific article; zbMATH DE number 1096053