On the remainder in the Weyl formula for the Euclidean disk

Yves Colin de Verdière (1)

1 IF - Institut Fourier

We prove a 2-terms Weyl formula for the counting function N(mu) of the spectrum of the Laplace operator in the Euclidean disk with a sharp remainder estimate O(mu^2/3).

Mots clés: lattice point problem; Laplace operator; eigenvalues; Weyl asymptotic formula; Bessel functions

Domaines: Physique mathématique [math-ph]; Théorie spectrale [math.SP]; Analyse classique [math.CA]

Yves Colin de Verdière. On the remainder in the Weyl formula for the Euclidean disk. 2011. ⟨hal-00585360v2⟩