By Nicolas Bergeron
text is an advent to the spectral idea of the Laplacian on
compact or finite sector hyperbolic surfaces. For a few of these
surfaces, known as “arithmetic hyperbolic surfaces”, the
eigenfunctions are of mathematics nature, and one may possibly use analytic
tools in addition to strong tools in quantity thought to review them.
an creation to the hyperbolic geometry of surfaces, with a
special emphasis on these of mathematics sort, after which an
introduction to spectral analytic tools at the Laplace operator on
these surfaces, the writer develops the analogy among geometry
(closed geodesics) and mathematics (prime numbers) in proving the
Selberg hint formulation. besides vital quantity theoretic
applications, the writer indicates functions of those instruments to the
spectral information of the Laplacian and the quantum unique
ergodicity estate. The latter refers back to the mathematics quantum
unique ergodicity theorem, lately proved by means of Elon Lindenstrauss.
fruit of numerous graduate point classes at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to check an array of classical effects and
then to be led in the direction of very lively parts in smooth mathematics.
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Extra info for The Spectrum of Hyperbolic Surfaces (Universitext)
The Spectrum of Hyperbolic Surfaces (Universitext) by Nicolas Bergeron