The spectral action on the noncommutative torus is obtained using a Chamseddine–Connes formula via computations of zeta functions. The importance of a Diophantine condition is outlined. Several results on holomorphic continuation of series of holomorphic functions are obtained in this context.
Cite this article
Driss Essouabri, Bruno Iochum, Cyril Levy, Andrzej Sitarz, Spectral action on noncommutative torus. J. Noncommut. Geom. 2 (2008), no. 1, pp. 53–123DOI 10.4171/JNCG/16