Author:
Cornelissen Gunther,Peyerimhoff Norbert
Abstract
AbstractWe study whether it is possible to apply twisted Laplace spectra (and, if so, how many are necessary) to deduce isometry of some well-known examples of isospectral manifolds in the literature, due to Schüth (simply connected manifolds), Ikeda (lens spaces), Vignéras/Linowitz and Voight (arithmetic surfaces), Milnor (lattice examples), Doyle and Rossetti (Tetra and Didi), Sunada (based on group-theoretical examples from Gerst, Gaßmann and Komatsu), Brooks and Tse (surfaces of small genus, Riemann surfaces of small genus), Barden and Kang (surfaces of genus two), and Miatello and Rossetti (flat manifolds isospectral for all twists by linear characters).
Publisher
Springer International Publishing
Reference20 articles.
1. Fawzi A.S. Al-Dukair (= Al-Thukair), Number Fields with Equal
L-series or Zeta Functions, Ph.D. thesis, University of California, Los Angeles (UCLA), 1981, viii+89 pp.
2. Jinpeng An, Jiu-Kang Yu and Jun Yu, On the dimension datum of a subgroup and its application to isospectral manifolds, J. Differential Geom. 94 (2013), no. 1, 59–85.
3. Dennis Barden and Hyunsuk Kang, Isospectral surfaces of genus two and three, Math. Proc. Cambridge Philos. Soc. 153 (2012), no. 1, 99–110.
4. Wieb Bosma, John Cannon, and Catherine Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. (Computational algebra and number theory (London, 1993)) 24 (1997), no. 3–4, 235–265, http://magma.maths.usyd.edu.au/magma/.
5. Robert Brooks, Constructing isospectral manifolds, Amer. Math. Monthly 95 (1988), no. 9, 823–839.