Computing the Continuous Discretely

Rubba, P.; Iannuzzi, Arcangelo; Postiglione, Alfredo; N, Scarpato; Montefusco, S; Gnasso, Agostino; Nappi, Gianantonio; Cortese, Claudio; Mancini, Mario

doi:10.1007/978-0-387-46112-0

Cited by 13 publications

(13 citation statements)

References 62 publications

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“…The function Ehr P (z) := k≥0 #(Z n ∩ kP)z k is called the Ehrhart series of P. By the Ehrhart Theorem for rational polytopes (see [BR,§3.7]), there exists a polynomial p(z) of degree less than q(n + 1) such that Ehr P (z) = p(z)/(1 − z q ) n+1 , which establishes the formula.…”

Section: Description Of Spectramentioning

confidence: 94%

Spectra of orbifolds with cyclic fundamental groups

Lauret

2016

Ann Glob Anal Geom

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Abstract. We give a simple geometric characterization of isospectral orbifolds covered by spheres, complex projective spaces and the quaternion projective line having cyclic fundamental group. The differential operators considered are Laplace-Beltrami operators twisted by characters of the corresponding fundamental group. To prove the characterization, we first give an explicit description of their spectra by using generating functions. We also include many isospectral examples.

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Section: Description Of Spectramentioning

confidence: 94%

Spectra of orbifolds with cyclic fundamental groups

Lauret

2016

Ann Glob Anal Geom

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“…. , v n ) as the sum of the d-volumes of the partitioning parallelotopes Z (S), leading to the following formula for the volume of a zonotope [5,1]: (Z (v 1 , . .…”

Section: Expected Number Of Vertices Of a Hypercube Slice Hunter Swanmentioning

confidence: 99%

“…. , v m ) which has dimension d can be partitioned into a number of parallelotopes [1], with one parallelotope for each maximal linearly independent subset S ⊆ {v 1 , . .…”

Section: Expected Number Of Vertices Of a Hypercube Slice Hunter Swanmentioning

confidence: 99%

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Expected Number of Vertices of a Hypercube Slice

Swan¹

2016

The American Mathematical Monthly

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“…Furthermore, it is well known that the Ehrhart series of an arbitrary rational polytope P can be written as Ehr P (z) = (1 − z q ) −(n+1) g(z) for some polynomial g(z) of degree less than q(n + 1), where n is the dimension of P and q is the smallest integer such that qP is integral (see for instance [BR,§3.7]). Theorem 6.2.…”

Section: Connections With Ehrhart Theory and Toric Varietiesmentioning

confidence: 99%

Recent results on the spectra of lens spaces

Miatello

Rossetti

2019

São Paulo J. Math. Sci.

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In this paper we report on recent results by several authors, on the spectral theory of lens spaces and orbifolds and similar locally symmetric spaces of rank one. Most of these results are related to those obtained by the authors in [IMRN (2016), 1054-1089], where the spectra of lens spaces were described in terms of the one-norm spectrum of a naturally associated congruence lattice. As a consequence, the first examples of Riemannian manifolds isospectral on p-forms for all p but not strongly isospectral were constructed.We also give a new elementary proof in the case of the spectrum on functions. In this proof, representation theory of compact Lie groups is avoided and replaced by the use of Molien's formula and a manipulation of the one-norm generating function associated to a congruence lattice. In the last four sections we present several recent results, open problems and conjectures on the subject.

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Computing the Continuous Discretely

Cited by 13 publications

References 62 publications

Spectra of orbifolds with cyclic fundamental groups

Spectra of orbifolds with cyclic fundamental groups

Expected Number of Vertices of a Hypercube Slice

Recent results on the spectra of lens spaces

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