Abstract
We define Dirichlet type series associated with homology length spectra of Riemannian, or Finsler, manifolds, or polyhedra, and investigate some of their analytical properties. As a consequence we obtain an inequality analogous to Gromov’s classical intersystolic inequality, but taking the whole homology length spectrum into account rather than just the systole.
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Partially supported by the Grants RFSF 10-01-00257-a, and ANR Finsler.
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Babenko, I., Massart, D. On systolic zeta functions. European Journal of Mathematics 3, 899–915 (2017). https://doi.org/10.1007/s40879-017-0181-1
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DOI: https://doi.org/10.1007/s40879-017-0181-1