Abstract
One gives an explicit bound of the number of isometry classes of flat tori isospectral to a given flat torus. The bound depends on the geometry of the given flat torus. These results hold in any dimension. In these case where dimension is two or three, one obtains bounds which only depend on the dimension.
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Berger M., Gauduchon P., Mazet E.—Le spectre d’une variété riemannienne, Lecture Notes in Math. Springer, 194, 1971
Berry J.P.—Tores isospectraux en dimension 3, C. R. Acad. Sci. Sér. I Math.,292 (1981), 163–166
Borel A.—Introduction aux groupes arithmétiques, Hermann, Actualités scientifiques et industrielles, 1341
Cassels J.W.S.—An introduction to the geometry of numbers, Springer, 1959
Kneser, M.—Lineare Relationen zwischen Darstellungszahlen quadratischer Formen, Math. Ann.,168 (1967), 31–39
Kitaoka Y.—Positive definite quadratic forms with same representation numbers, Arch. Math.,28 (1977), 495–497
Lekerkerker C.G.—Geometry of numbers, Wolters-Noordhoff, 1969
Milnor J.—Eigenvalue of the Laplace operator on certain manifolds, Proc. Nat. Acad. Sci.,51 (1964), 542
Wolpert S.—The eigenvalue spectrum as moduli for flat tori, Trans. Amer. Math. Soc.,244 (1978), 312–321
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Cette recherche a été faite en partie dans le cadre du contrat C.E.E. “GADGET” SC1-0105-C au laboratoire associé au C.N.R.S., no188
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Pesce, H. Borne explicite du nombre de tores plats isospectraux à un tore donné. Manuscripta Math 75, 211–223 (1992). https://doi.org/10.1007/BF02567081
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DOI: https://doi.org/10.1007/BF02567081