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Isospectral congruence manifolds, spectral rigidity, and a converse to Vignéras
Let $B$ be a quaternion division algebra over a number field $k$ that gives rise to arithmetic Fuchsian or Kleinian groups, and let $\mathcal{O}$ be a maximal order of $B$. We show that every closed orientable Riemannian manifold isospectral to a principal congruence hyperbolic surface $X_\mathcal{O
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