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Riemannian Coverings and Isospectral Manifolds

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/cpa.3160250302openalex-snapshot
Selberg's trace formula as applied to a compact riemann surface
inferredcites →https://doi.org/10.1007/978-1-4684-9458-7openalex-snapshot
Linear Representations of Finite Groups
inferredcites →https://doi.org/10.1007/978-3-642-57956-1openalex-snapshot
Basic Algebraic Geometry 2
inferredcites →https://doi.org/10.1007/bfb0061302openalex-snapshot
The Selberg Trace Formula for PSL(2,ℝ)
inferredcites →https://doi.org/10.1090/s0002-9904-1963-11001-0openalex-snapshot
Maximal Fuchsian groups
inferredcites →https://doi.org/10.1090/s0002-9904-1974-13609-8openalex-snapshot
Small eigenvalues of the Laplace operator on compact Riemann surfaces
inferredcites →https://doi.org/10.1215/ijm/1256049498openalex-snapshot
Zeta functions of Selberg's type for compact space forms of symmetric spaces of rank one
inferredcites →https://doi.org/10.1515/9781400869862-013openalex-snapshot
43. On Deformations of Complex Analytic Structures, I
inferredcites →https://doi.org/10.1515/9781400881550-038openalex-snapshot
The Length Spectrum as Moduli for Compact Riemann Surfaces
inferredcites →https://doi.org/10.18311/jims/1956/16985openalex-snapshot
Harmonic Analysis and Discontinuous Groups in Weakly Symmetric Riemannian Spaces With Applications to Dirichlet Series
inferredcites →https://doi.org/10.2307/1971319openalex-snapshot
Varietes Riemanniennes Isospectrales et non Isometriques
inferredcites →https://doi.org/10.2307/2006982openalex-snapshot
An Analogue of the Prime Number Theorem for Closed Orbits of Axiom a Flows
inferredcites →https://doi.org/10.2969/jmsj/02740600openalex-snapshot
A characterization of arithmetic Fuchsian groups
inferredcites →https://doi.org/10.2969/jmsj/03530437openalex-snapshot
On spherical space forms which are isospectral but not isometric
inferredcites →https://doi.org/10.2996/kmj/1138847384openalex-snapshot
On the adele rings of algebraic number fields
inferredcites →https://doi.org/10.4064/aa-17-2-121-139openalex-snapshot
On the theory of nth power residues and a conjecture of Kronecker

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Triple Products of Eigenfunctions and Spectral Geometry
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Generation of isospectral graphs
inferred← citeshttps://doi.org/10.1002/cpa.3160400306openalex-snapshot
Isospectral deformations I: Riemannian structures on two‐step nilspaces
inferred← citeshttps://doi.org/10.1002/cpa.3160420803openalex-snapshot
Isospectral deformations II: Trace formulas, metrics, and potentials
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Mutually Isospectral Riemann Surfaces
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Quantum graphs which sound the same
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Inverse spectral problems on compact Riemannian manifolds
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Inverse spectral problems in riemannian geometry
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Spectral Theory
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Basic Analysis of Regularized Series and Products
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Artin formalism and heat kernels
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You Can’t Hear the Shape of a Manifold
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Isospectral potentials on a surface of Genus 3
inferred← citeshttps://doi.org/10.1007/978-1-4614-1939-6openalex-snapshot
Spectra of Graphs
inferred← citeshttps://doi.org/10.1007/978-1-4614-6325-2_3openalex-snapshot
Artin Formalism and Heat Kernels
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Flat Space: Fourier Analysis on $${\mathbb{R}}^{m}$$
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A Compact Symmetric Space: The Sphere
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The Poincaré Upper Half-Plane
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On the Construction of Isospectral Manifolds
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Spectral Theory
inferred← citeshttps://doi.org/10.1007/978-1-4757-6720-9_13openalex-snapshot
Length and Torsion in Arithmetic Hyperbolic Orbifolds
inferred← citeshttps://doi.org/10.1007/978-3-030-04161-8_18openalex-snapshot
How to Hear the Corners of a Drum
inferred← citeshttps://doi.org/10.1007/978-3-031-27704-7openalex-snapshot
Twisted Isospectrality, Homological Wideness, and Isometry
inferred← citeshttps://doi.org/10.1007/978-3-031-27704-7_1openalex-snapshot
Introduction
inferred← citeshttps://doi.org/10.1007/978-3-031-27704-7_10openalex-snapshot
Homological Wideness, “Class Field Theory” for Covers, and a Number Theoretical Analogue
inferred← citeshttps://doi.org/10.1007/978-3-031-27704-7_11openalex-snapshot
Examples Concerning the Main Result
inferred← citeshttps://doi.org/10.1007/978-3-031-27704-7_3openalex-snapshot
Spectra, Group Representations and Twisted Laplacians
inferred← citeshttps://doi.org/10.1007/978-3-031-27704-7_4openalex-snapshot
Detecting Representation Isomorphism Through Twisted Spectra
inferred← citeshttps://doi.org/10.1007/978-3-031-62014-0_1openalex-snapshot
Lecture Notes on Birkhoff Billiards: Dynamics, Integrability and Spectral Rigidity
inferred← citeshttps://doi.org/10.1007/978-3-031-66612-4_1openalex-snapshot
Introduction and Main Results
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Distribution Kernel of Analytic Semigroups in the Hypoelliptic Case
inferred← citeshttps://doi.org/10.1007/978-3-031-81217-0_6openalex-snapshot
My Journey in Geometry
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Spectral Geometry: An Introduction and Background Material for this Volume
inferred← citeshttps://doi.org/10.1007/978-3-0348-8938-4_3openalex-snapshot
Spectral Geometry on Nilmanifolds
inferred← citeshttps://doi.org/10.1007/978-3-0348-8938-4_5openalex-snapshot
Construction de Variétés Isospectrales Autour du Théorème de T. Sunada
inferred← citeshttps://doi.org/10.1007/978-3-0348-8938-4_8openalex-snapshot
Inverse Spectral Geometry
inferred← citeshttps://doi.org/10.1007/978-3-0348-8938-4_9openalex-snapshot
Inverse Spectral Geometry on Riemann Surfaces
inferred← citeshttps://doi.org/10.1007/978-3-0348-9110-3_5openalex-snapshot
Spectral Theory and Geometry
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Spectral Theory and Geometry
inferred← citeshttps://doi.org/10.1007/978-3-319-61860-9_4openalex-snapshot
Chapter 4 Connections and Curvature
inferred← citeshttps://doi.org/10.1007/978-3-642-21298-7_4openalex-snapshot
Chapter 4 Connections and Curvature
inferred← citeshttps://doi.org/10.1007/978-3-642-55627-2_4openalex-snapshot
Constructing Isospectral Metrics via Principal Connections
inferred← citeshttps://doi.org/10.1007/978-3-642-77303-7_1openalex-snapshot
Recent Progress in Classical Mechanics
inferred← citeshttps://doi.org/10.1007/978-3-642-78502-3_22openalex-snapshot
Some Trends in Riemannian Geometry
inferred← citeshttps://doi.org/10.1007/978-3-662-08966-8_10openalex-snapshot
Stability and Reconstruction in Gel’fand Inverse Boundary Spectral Problem
inferred← citeshttps://doi.org/10.1007/978-3-7643-9921-4_19openalex-snapshot
Remark on Spectral Rigidity for Magnetic Schrödinger Operators
inferred← citeshttps://doi.org/10.1007/978-4-431-54177-6_1openalex-snapshot
Introduction
inferred← citeshttps://doi.org/10.1007/978-4-431-54177-6_10openalex-snapshot
Discrete Abel–Jacobi Maps
inferred← citeshttps://doi.org/10.1007/978-4-431-54177-6_2openalex-snapshot
Quotient Objects
inferred← citeshttps://doi.org/10.1007/978-4-431-54177-6_3openalex-snapshot
Generalities on Graphs
inferred← citeshttps://doi.org/10.1007/978-4-431-54177-6_4openalex-snapshot
Homology Groups of Graphs
inferred← citeshttps://doi.org/10.1007/978-4-431-54177-6_5openalex-snapshot
Covering Graphs
inferred← citeshttps://doi.org/10.1007/978-4-431-54177-6_6openalex-snapshot
Topological Crystals
inferred← citeshttps://doi.org/10.1007/978-4-431-54177-6_7openalex-snapshot
Standard Realizations
inferred← citeshttps://doi.org/10.1007/978-4-431-54177-6_8openalex-snapshot
Explicit Construction
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Random Walks on Topological Crystals
inferred← citeshttps://doi.org/10.1007/978-4-431-68168-7_5openalex-snapshot
Spectral Invariants of Conformal Metrics
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Are Scattering Properties of Networks Uniquely Connected to Their Shapes?
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S
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Isospectral Closed Riemannian Manifolds
inferred← citeshttps://doi.org/10.1007/978-94-017-2475-3_5openalex-snapshot
Spectral Properties of the Laplacians for the de Rham Complex
inferred← citeshttps://doi.org/10.1007/978-981-15-8199-1_2openalex-snapshot
Multi-Dimensional Inverse Boundary Value Problems
inferred← citeshttps://doi.org/10.1007/bf01200435openalex-snapshot
Small volume isospectral, non-isometric, hyperbolic 2-orbifolds
inferred← citeshttps://doi.org/10.1007/bf01231320openalex-snapshot
Isospectral plane domains and surfaces via Riemannian orbifolds
inferred← citeshttps://doi.org/10.1007/bf01232028openalex-snapshot
Spectral geometry and scattering theory for certain complete surfaces of finite volume
inferred← citeshttps://doi.org/10.1007/bf01444635openalex-snapshot
Transplantation et isospectralité. I
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Isospectrality and galois projective geometries
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Spectral geometry in dimension 3
inferred← citeshttps://doi.org/10.1007/bf02565837openalex-snapshot
On Cheeger's inequality
inferred← citeshttps://doi.org/10.1007/bf02566419openalex-snapshot
Représentations relativement équivalentes et variétés riemanniennes isospectrales
inferred← citeshttps://doi.org/10.1007/bf02566421openalex-snapshot
The marked length spectrum vs. the Laplace spectrum on forms on Riemannian nilmanifolds
inferred← citeshttps://doi.org/10.1007/bf02566599openalex-snapshot
Rigidity for surfaces of non-positive curvature
inferred← citeshttps://doi.org/10.1007/bf02566766openalex-snapshot
The geometry and spectrum of the one holed torus
inferred← citeshttps://doi.org/10.1007/bf02570886openalex-snapshot
Isospectral connections on line bundles
inferred← citeshttps://doi.org/10.1007/bf02921826openalex-snapshot
Continuous families of Riemannian manifolds, Isospectral on functions but not on 1-forms
inferred← citeshttps://doi.org/10.1007/bf02921882openalex-snapshot
Length spectra andp-spectra of compact flat manifolds
inferred← citeshttps://doi.org/10.1007/bf02930699openalex-snapshot
Isospectral potentials and conformally equivalent isospectral metrics on spheres, balls and Lie groups
inferred← citeshttps://doi.org/10.1007/bf02930761openalex-snapshot
Flat manifolds isospectral on p-forms
inferred← citeshttps://doi.org/10.1007/bf02930995openalex-snapshot
Isoscattering on surfaces
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On the conjugacy of element-conjugate homomorphisms
inferred← citeshttps://doi.org/10.1007/bf03025190openalex-snapshot
When you can’t hear the shape of a manifold
inferred← citeshttps://doi.org/10.1007/bf03025191openalex-snapshot
Sphere and torus music
inferred← citeshttps://doi.org/10.1007/bf03322715openalex-snapshot
Isospectrality for Spherical Space Forms
inferred← citeshttps://doi.org/10.1007/bfb0075662openalex-snapshot
L-functions in geometry and some applications
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Basic Analysis of Regularized Series and Products
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Number theoretic analogues in spectral geometry
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Cayley graphs and planar isospectral domains
inferred← citeshttps://doi.org/10.1007/bfb0083055openalex-snapshot
Density theorems for closed orbits
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Fundamental groups and Laplacians
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Limit constructions over Riemann surfaces and their parameter spaces, and the commensurability group actions
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Isospectral simply-connected homogeneous spaces and the spectral rigidity of group actions
inferred← citeshttps://doi.org/10.1007/s00013-006-1748-0openalex-snapshot
One cannot hear orbifold isotropy type
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Equivariant isospectrality and Sunada’s method
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The G-invariant spectrum and non-orbifold singularities
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The Neumann Isospectral Problem for Trapezoids
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On Spectral Minimal Partitions: A Survey
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Isoscattering Schottky manifolds
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Locally Non-isometric yet Super Isospectral Spaces
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Coarse non-amenability and covers with small eigenvalues
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Isometries of Lorentz surfaces and convergence groups
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Interrogating surface length spectra and quantifying isospectrality
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On systoles and ortho spectrum rigidity
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Unmarked simple length spectral rigidity for covers
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Spin structures and spectra of Z 2 k -manifolds
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Spectral decomposition of square-tiled surfaces
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Small isospectral and nonisometric orbifolds of dimension 2 and 3
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Integral Gassman equivalence of algebraic and hyperbolic manifolds
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Spectral theory of a class of nilmanifolds attached to Clifford modules
inferred← citeshttps://doi.org/10.1007/s00209-021-02758-yopenalex-snapshot
One can't hear orientability of surfaces
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Free Energy as a Dynamical Invariant (or Can You Hear the Shape of a Potential?)
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Free Energy as a Geometric Invariant
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Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards
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Isophasal Scattering Manifolds in Two Dimensions
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Length spectra and degeneration of flat metrics
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Counting and effective rigidity in algebra and geometry
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A fast modal space transform for robust nonrigid shape retrieval
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Weakly commensurable arithmetic groups and isospectral locally symmetric spaces
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Duality Questions for Operators, Spectrum and Measures
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Isospectral orbifolds with different maximal isotropy orders
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Short-time behavior of the heat kernel and Weyl’s law on $${{\mathrm{RCD}}}^*(K,N)$$ RCD ∗ ( K , N ) spaces
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On the Poisson relation for compact Lie groups
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Isospectral surfaces with distinct covering spectra via Cayley graphs
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The Sunada construction and the simple length spectrum
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The spectrum on p-forms of a lens space
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Characterizing covers via simple closed curves
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Isospectral Domains for Discrete Elliptic Operators
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Heraclitus-Maximal Worlds
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Can one hear the spanning trees of a quantum graph?
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Local audibility of a hyperbolic metric
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Trace of heat kernel, spectral zeta function and isospectral problem for sub-laplacians
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Isospectral nearly Kähler manifolds
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Linear Representations and Isospectrality with Boundary Conditions
inferred← citeshttps://doi.org/10.1007/s12220-019-00196-1openalex-snapshot
On the Spectrum of Differential Operators Under Riemannian Coverings
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Isospectral CR Manifolds with Respect to the Kohn Laplacian
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Some recent developments on the Steklov eigenvalue problem
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A geometric construction of isospectral magnetic graphs
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Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator
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Non-isometric Riemannian G-Manifolds with Equal Equivariant Spectra
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Twisted Perron-Frobenius theorem and L-functions
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Compact isospectral sets of surfaces
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Homology, Wiener integrals, and integrated densities of states
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On manifolds of negative curvature with isospectral potentials
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On isospectral potentials on a discrete lattice II
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Determinants of Laplacians; Heights and Finiteness
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The spectral geometry of operators of Dirac and Laplace type
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Transplantation and Jacobians of Sunada isospectral Riemann surfaces
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Equivariant inverse spectral theory and toric orbifolds
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Discrete homotopies and the fundamental group
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Diffusion determines the recurrent graph
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A refined notion of arithmetically equivalent number fields, and curves with isomorphic Jacobians
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Counting isospectral manifolds
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Nearby special Lagrangians
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Spectral problems with mixed Dirichlet–Neumann boundary conditions: Isospectrality and beyond
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Bounded gaps between primes and the length spectra of arithmetic hyperbolic 3-orbifolds
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Constructing cospectral bipartite graphs
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Constructing cospectral graphs via regular rational orthogonal matrices with level two
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An improved condition for a family of trees being determined by their generalized spectrum
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Constructing cospectral graphs via regular rational orthogonal matrix with level two and three
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Zeta functions that hear the shape of a Riemann surface
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Z2 -cohomology and spectral properties of flat manifolds of diagonal type
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On a relation between spectral theory of lens spaces and Ehrhart theory
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Small linearly equivalent G-sets and a construction of Beaulieu
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Corresponding Abelian extensions of integrally equivalent number fields
inferred← citeshttps://doi.org/10.1016/j.joems.2011.09.003openalex-snapshot
Introduction to some conjectures for spectral minimal partitions
inferred← citeshttps://doi.org/10.1016/j.laa.2016.05.021openalex-snapshot
Line graphs and the transplantation method
inferred← citeshttps://doi.org/10.1016/j.laa.2018.10.027openalex-snapshot
Cospectral graphs, GM-switching and regular rational orthogonal matrices of level p
inferred← citeshttps://doi.org/10.1016/j.laa.2020.05.025openalex-snapshot
On a theorem of Godsil and McKay concerning the construction of cospectral graphs
inferred← citeshttps://doi.org/10.1016/j.laa.2023.03.025openalex-snapshot
Acceptability of classical groups in non-zero characteristic
inferred← citeshttps://doi.org/10.1016/j.laa.2025.01.033openalex-snapshot
Constructing adjacency and distance cospectral graphs via regular rational orthogonal matrix
inferred← citeshttps://doi.org/10.1016/j.matpur.2008.02.009openalex-snapshot
Inverse spectral problems on a closed manifold
inferred← citeshttps://doi.org/10.1016/j.topol.2015.11.006openalex-snapshot
A universal Riemannian foliated space
inferred← citeshttps://doi.org/10.1016/s0022-314x(02)00053-7openalex-snapshot
On an Archimedean analogue of Tate's conjecture
inferred← citeshttps://doi.org/10.1016/s0040-9383(96)00028-6openalex-snapshot
Compacité de l'ensemble des réseaux isospectraux et conséquences
inferred← citeshttps://doi.org/10.1016/s1874-5741(00)80009-6openalex-snapshot
Survey of Isospectral Manifolds
inferred← citeshttps://doi.org/10.1017/9781009701730.004openalex-snapshot
The Klein Quartic in Number Theory
inferred← citeshttps://doi.org/10.1017/etds.2021.37openalex-snapshot
Inverse problems and rigidity questions in billiard dynamics
inferred← citeshttps://doi.org/10.1017/fms.2015.33openalex-snapshot
COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES
inferred← citeshttps://doi.org/10.1017/psa.2024.53openalex-snapshot
What Do Privileged Coordinates Tell Us about Structure?
inferred← citeshttps://doi.org/10.1017/s0013091524000579openalex-snapshot
Gassmann triples with special cycle types and applications
inferred← citeshttps://doi.org/10.1017/s0027763000002518openalex-snapshot
Isospectral surfaces of small genus
inferred← citeshttps://doi.org/10.1017/s0143385707000557openalex-snapshot
An analogue of Bauer’s theorem for closed orbits of skew products
inferred← citeshttps://doi.org/10.1017/s0305004107000758openalex-snapshot
Spectral rigidity and discreteness of 2233-groups
inferred← citeshttps://doi.org/10.1017/s0305004112000126openalex-snapshot
Isospectral surfaces of genus two and three
inferred← citeshttps://doi.org/10.1023/a:1000286121144openalex-snapshot
Une réciproque générique du théorème Sunada
inferred← citeshttps://doi.org/10.1023/a:1015651821995openalex-snapshot
Comparison of Twisted P-Form Spectra for Flat Manifolds with Diagonal Holonomy
inferred← citeshttps://doi.org/10.1023/b:simj.0000042478.24379.8bopenalex-snapshot
Isospectral Flat 3-Manifolds
inferred← citeshttps://doi.org/10.1038/s41598-020-80950-6openalex-snapshot
Isoscattering strings of concatenating graphs and networks
inferred← citeshttps://doi.org/10.1038/s41598-025-23400-5openalex-snapshot
Isoscattering non-isospectral quantum graphs
inferred← citeshttps://doi.org/10.1063/1.1557330openalex-snapshot
Boundary behavior of quantum Green’s functions
inferred← citeshttps://doi.org/10.1063/1.5016648openalex-snapshot
The first two largest eigenvalues of Laplacian, spectral gap problem and Cheeger constant of graphs
inferred← citeshttps://doi.org/10.1080/00029890.1988.11972094openalex-snapshot
Constructing Isospectral Manifolds
inferred← citeshttps://doi.org/10.1080/00927879408824882openalex-snapshot
Subgroups of finitep-groups inducing the same permutation character
inferred← citeshttps://doi.org/10.1080/03605309208820840openalex-snapshot
Kuznecov Sum Formulae and Szegˇ Limit Formulae on Manifolds
inferred← citeshttps://doi.org/10.1080/03605309508821109openalex-snapshot
On isospectral potentials on flat tori II
inferred← citeshttps://doi.org/10.1080/17476930802315157openalex-snapshot
Towers of isospectral manifolds
inferred← citeshttps://doi.org/10.1086/739249openalex-snapshot
Determinism and Asymmetry in General Relativity
inferred← citeshttps://doi.org/10.1088/0305-4470/34/30/303openalex-snapshot
Equivalence between isospectrality and isolength spectrality for a certain class of planar billiard domains
inferred← citeshttps://doi.org/10.1088/0305-4470/34/31/301openalex-snapshot
Can one hear the shape of a graph?
inferred← citeshttps://doi.org/10.1088/0305-4470/37/33/009openalex-snapshot
Isospectral membranes: a connection between shape and density
inferred← citeshttps://doi.org/10.1088/0305-4470/37/7/016openalex-snapshot
Diffractive orbits in isospectral billiards
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