The blowup along the diagonal of the spectral function of the Laplacian
  We formulate a precise conjecture about the universal behavior near the diagonal of the spectral function of the Laplacian of a smooth compact Riemann manifold. We prove this conjecture when the manifold and the metric are real analytic, and we also present an alternate proof when the manifold is the round sphere. 
Liviu I. Nicolaescu
math.DG math-ph math.AP math.MP