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Holomorphic torsion with coefficients and geometric zeta functions for certain Hermitian locally symmetric manifolds

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  • Henri Moscovici, Ohio State University, Columbus, USA
  • Robert J. Stanton, Ohio State University, Columbus, USA
  • Jan Frahm
We give a dynamical description, in terms of a Weil-type zeta function, to the holomorphic torsion with coefficients for certain compact Hermitian locally symmetric manifolds, whose connected group G of isometries of the universal cover has only one conjugacy class of cuspidal maximal parabolic subgroup and also satisfies a technical Ansatz relative to the given coefficients. The two senior authors are indebted to their junior colleague, Jan Frahm, for his laborious work shedding light on the scope of the validity of the Ansatz, and for writing up the attached Appendix. The results therein show that for real rank one groups G the Ansatz is satisfied with respect to any coefficients, for some rank two groups G it is satisfied with respect to certain coefficients, and also that there are groups G which do not obey the Ansatz.
StatusAfsendt - 2018


  • math.RT, math.DG

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