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This article is about inverse spectral problems for hyperbolic surfaces andin particular how length spectra relate to the geometry of the underlyingsurface. A quantitative answer is given to the following: how many questions doyou need to ask a length spectrum to determine it completely? In answeringthis, a quantitative upper bound is given on the number of isospectral butnon-isometric surfaces of a given genus.

Interrogating surface length spectra and quantifying isospectrality