Meromorphic continuation approach to noncommutative geometry

Franck Gautier-Baudhuit (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

Following an idea of Nigel Higson, we develop a method for proving the existence of a meromor-phic continuation for some spectral zeta functions. The method is based on algebras of generalized differential operators. The main theorem states, under some conditions, the existence of a meromor-phic continuation, a localization of the poles in supports of arithmetic sequences and an upper bound of their order. We give an application in relation with a class of nilpotent Lie algebras.

Mots clés: Zeta function; Meromorphic continuation; nilpotent Lie algebra; Differential operator

Domaines: Analyse fonctionnelle [math.FA]; Théorie spectrale [math.SP]; Algèbres d'opérateurs [math.OA]

Franck Gautier-Baudhuit. Meromorphic continuation approach to noncommutative geometry. 2016. ⟨hal-01396922⟩