author={Robert Brooks and Ruth Gornet and William Gustafson},
  journal={Advances in Mathematics},
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… 
Spectral rigidity and discreteness of 2233-groups
Abstract In this paper we describe methods for dealing with the trace spectrum of a subgroup of PSL(2, $\mathbb{R}$) generated by four elliptic elements α, β, γ, δ of respective orders 2, 2, 3, 3,
Isospectral metrics and potentials on classical compact simple Lie groups
Given a compact Riemannian manifold (M, g), the eigenvalues of the Laplace operator � form a discrete sequence known as the spectrum of (M, g). (In the case the M has boundary, we stipulate either
Z k 2 -Manifolds are isospectral on forms
We obtain a simple formula for the multiplicity of eigenvalues of the Hodge- Laplace operator, � f , acting on sections of the full exterior bundle � ∗ (TM) = � n=0 � p (TM) over an arbitrary compact
Counting isospectral manifolds
Isospectral and Isoscattering Manifolds: A Survey of Techniques and Examples
The method of torus actions developed by the flrst and third au- thors yields examples of isospectral, non-isometric metrics on compact mani- folds and isophasal, non-isometric metrics on non-compact
Families of mutually isospectral Riemannian orbifolds
In this paper, we consider three arithmetic families of isospectral non‐isometric Riemannian orbifolds and in each case derive an upper bound for the size of the family which is polynomial as a
Isospectral potentials and conformally equivalent isospectral metrics on spheres, balls and Lie groups
We construct pairs of conformally equivalent isospectral Riemannian metrics ϕ1g and ϕ2g on spheres Sn and balls Bn+1 for certain dimensions n, the smallest of which is n=7, and on certain compact
Constructing isospectral manifolds
In this article we construct nonisometric, isospectral manifolds modelled on semisimple Lie groups with finite center and no compact factors. Specifically, our two main results are the construction


Maximal Fuchsian groups
1. DEFINITIONS. Let D be the unit disk {z\ \z\ < l } and let £ be the group of conformai homeomorphisms of D. A Fuchsian group is a discrete subgroup of <£. We shall be concerned here with the
Geometry and Spectra of Compact Riemann Surfaces
This book discusses hyperbolic structures, closed Geodesics and Huber's Theorem, and perturbations of the Laplacian in Hilbert Space.
Topics in Galois Theory
This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions
Isospectral deformations I: Riemannian structures on two‐step nilspaces
On montre comment construire des exemples de deformations isospectrales de metriques de Riemann sur des varietes sur lesquelles des recouvrements de certains groupes de Lie nilpotents agissent
Non-Sunada graphs
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Konstruktion von Zahlkörpern mit gegebener Galoisgruppe von Primzahlpotenzordnung.
Es soll hier die Aufgabe gelöst werden, über einem gegebenen Zahlkörper endlichen Grades einen Körper zu konstruieren, der normal über mit einer zu einer gegebenen Gruppe © von ungerader