On the Hofer–Zehnder conjecture on weighted projective spaces

We prove an extension of the homology version Hofer–Zehnder conjecture proved by Shelukhin to weighted projective spaces which are symplectic orbifolds. In particular, we that if number fixed points counted with their isotropy order as multiplicity a non-degenerate Hamiltonian diffeomorphism such space is larger than minimum possible, then there infinitely many periodic points.