Distribution |detx| on p-adic matrices
نویسنده
چکیده
where d×x denotes a Haar measure on G. Up to constants, for (additive) Haar measure dx on A, d×x = dx/|detx|. For brevity, write |x| for |detx| when possible. [0.1] Convergence The integral defining us converges absolutely in Re(s) > n− 1: Recall the Iwasawa decomposition G = P ·K with P the parabolic subgroup of upper-triangular matrices. Since K is open in G, Haar measure on G restricted to K is Haar measure on K. Recall the integral formula ∫
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