Integral Riemann-Roch formulae for cyclic subgroups of mapping class   groups
  The first author conjectured certain relations for Morita-Mumford classes and Newton classes in the integral cohomology of mapping class groups (integral Riemann-Roch formulae). In this paper, the conjecture is verified for cyclic subgroups of mapping class groups. 
Toshiyuki Akita and Nariya Kawazumi