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Displaying similar documents to “Eigenfunctions of the laplacian, quantum chaos, and computation”

From pseudodifferential analysis to modular form theory

André Unterberger (1999)

Journées équations aux dérivées partielles

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Taking advantage of methods originating with quantization theory, we try to get some better hold - if not an actual construction - of Maass (non-holomorphic) cusp-forms. We work backwards, from the rather simple results to the mostly devious road used to prove them.

Quantum unique ergodicity for Eisenstein series on P S L 2 ( ℤ ∖ P S L 2 ( ℝ )

Dmitry Jakobson (1994)

Annales de l'institut Fourier

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In this paper we prove microlocal version of the equidistribution theorem for Wigner distributions associated to Eisenstein series on P S L 2 ( ℤ ) ∖ P S L 2 ( ℝ ) . This generalizes a recent result of W. Luo and P. Sarnak who proves equidistribution for P S L 2 ( ℤ ) ∖ ℍ . The averaged versions of these results have been proven by Zelditch for an arbitrary finite-volume surface, but our proof depends essentially on the presence of Hecke operators and works only for congruence subgroups of S L 2 ( ℝ ) . In the proof the key estimates come...

Application of linear hyperbolic PDE to linear quantum fields in curved spacetimes : especially black holes, time machines and a new semi-local vacuum concept

Bernard Kay (2000)

Journées équations aux dérivées partielles

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Several situations of physical importance may be modelled by linear quantum fields propagating in fixed spacetime-dependent classical background fields. For example, the quantum Dirac field in a strong and/or time-dependent external electromagnetic field accounts for the creation of electron-positron pairs out of the vacuum. Also, the theory of linear quantum fields propagating on a given background curved spacetime is the appropriate framework for the derivation of black-hole evaporation...

Trace formulae and applications to class numbers

Nicole Raulf (2014)

Open Mathematics

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In this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL2( 𝒪 K ) with 𝒪 K being the ring of integers of an imaginary quadratic number field K of class number H K > 1. Furthermore, as a corollary we obtain an asymptotic result for class numbers of binary quadratic forms.