Weyl expansion of a circle billiard in a magnetic field

We compute the high orders of the Weyl expansion for the heat kernel of a c ircle billiard in the presence of a uniform and perpendicular magnetic fiel d. It is shown, in accordance with a conjecture made in Narevich et al (199 8 J. Phys. A: Math. Gen. 31 4277), that some terms of this expansion can be identified with those of the Weyl expansion of a semi-infinite cylinder. T he boundary correction to the Landau diamagnetic susceptibility of a non-de generate electron gas in the billiard is determined.