Une remarque sur les intégrales orbitales de la fonction caractéristique d'un réseau hyperspécial de gl(n)gl(n)

Let F   be a non-archimedean field, let g=gl(n,F)g=gl(n,F) and let kk be the lattice of matrices whose coefficients are integers. Consider a function f   on gg whose orbital integrals are supported on elements with integral eigenvalues and such that the Fourier transform of f has the same property. Then the orbital integrals of f   are equal to the orbital integrals of the characteristic function of kk, up to a constant.