On the asymptotics of the on-diagonal Szeg\"o kernel of certain   Reinhardt domains
  We compute the leading and sub-leading terms in the asymptotic expansion of the Szeg\"o kernel on the diagonal of a class of pseudoconvex Reinhardt domains whose boundaries are endowed with a general class of smooth measures. We do so by relating it to a Bergman kernel over projective space. 
Arash Karami and Vamsi Pingali
math.CV math.DG