  This is a report on a joint work [12] with D. Essouabri, C. Levy and A.
Sitarz. The spectral action on noncommutative torus is obtained, using a
Chamseddine--Connes formula via computations of zeta functions. The importance
of a Diophantine condition is outlined as far as the difficulties to go beyond.
Some results on holomorphic continuation of series of holomorphic functions are
presented.
