MUTUALLY ISOSPECTRAL RIEMANN SURFACES

@article{Brooks1998MUTUALLYIR,
  title={MUTUALLY ISOSPECTRAL RIEMANN SURFACES},
  author={Robert Brooks and Ruth Gornet and William Gustafson},
  journal={Advances in Mathematics},
  year={1998},
  volume={138},
  pages={306-322}
}
In this paper, we address the following question: given a natural number g, how many Riemann surfaces S 1 ; : : :; S k of genus g can there be such that S 1 ; : : :; S k all share the same spectrum of the Laplacian? It was shown by Buser in Bu] that there is an upper bound N(g) to the size of such isospectral sets, depending only on the genus. More precisely, he gave the following upper estimate for N(g): Theorem 0.1 ((Bu]) N(g) e 720g 2. The problem of nding a lower bound for N(g) was… 
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