Soit une surface hyperbolique non compacte à volume fini sans points elliptiques, et soit l’opérateur de diffusion de Lax–Phillips. En utilisant l’approche due à Voros sur la fonction superzeta, nous définissons une fonction zêta de type Hurwitz construite à partir des résonances associées à . Nous prouvons le prolongement méromorphe en le paramètre de et, en utilisant la valeur spéciale à , définissons un déterminant des opérateurs . Nous obtenons des expressions pour la fonction zêta de Selberg et le déterminant de la matrice de diffusion en termes de déterminants d’opérateurs.
Let denote a finite volume, non-compact hyperbolic surface without elliptic points, and let denote the Lax–Phillips scattering operator. Using the superzeta function approach due to Voros, we define a Hurwitz-type zeta function constructed from the resonances associated to . We prove the meromorphic continuation in of and, using the special value at , define a determinant of the operators . We obtain expressions for Selberg’s zeta function and the determinant of the scattering matrix in terms of the operator determinants.
Révisé le : 2018-03-21
Accepté le : 2019-08-19
Publié le : 2020-12-18
Classification : 11M36
Mots clés : régularisation super-zêta, fonction zêta de Selberg, déterminant de dispersion, noyau de la chaleur, métrique hyperbolique
@article{AIF_2020__70_3_915_0, author = {Friedman, Joshua S. and Jorgenson, Jay and Smajlovi\'c, Lejla}, title = {The determinant of the Lax--Phillips scattering operator}, journal = {Annales de l'Institut Fourier}, pages = {915--947}, publisher = {Association des Annales de l'institut Fourier}, volume = {70}, number = {3}, year = {2020}, doi = {10.5802/aif.3327}, language = {en}, url = {aif.centre-mersenne.org/item/AIF_2020__70_3_915_0/} }
Friedman, Joshua S.; Jorgenson, Jay; Smajlović, Lejla. The determinant of the Lax–Phillips scattering operator. Annales de l'Institut Fourier, Tome 70 (2020) no. 3, pp. 915-947. doi : 10.5802/aif.3327. https://aif.centre-mersenne.org/item/AIF_2020__70_3_915_0/
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