The spectrum on $p$-forms of a lens space

Abstract

We give an explicit description of the spectrum of the Hodge--Laplace operator on $p$-forms of an arbitrary lens space for any $p$. We write the two generating functions encoding the $p$-spectrum as rational functions. As a consequence, we prove a geometric characterization of lens spaces that are $p$-isospectral for every $p$ in an interval of the form $[0,p_0]$.

Accepted in Geom. Dedicata, February 2018

References in corpus (5)

• Spectra of orbifolds with cyclic fundamental groups
• Spectra of lens spaces from 1-norm spectra of congruence lattices
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• Non-strongly isospectral spherical space forms
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Cited by in corpus (4)

• Higher spin partition functions via the quasinormal mode method in de Sitter quantum gravity
• A computational study on lens spaces isospectral on forms
• Recent results on the spectra of lens spaces
• Weight multiplicity formulas for bivariate representations of classical Lie algebras