The function epsilon for complex tori and Riemann surfaces (Q1580687)

In the framework of the quantization of Kähler manifolds, studied by \textit{M. Cahen, S. Gutt} and \textit{J. H. Rawnsley} in a series of papers [J. Geom. Phys. 7, No. 1, 45-62 (1990; Zbl 0719.53044), Trans. Am. Math. Soc. 337, No. 1, 73-98 (1993; Zbl 0788.53062), Lett. Math. Phys. 30, No. 4, 291-305 (1994; Zbl 0826.53052), 34, No. 2, 159-168 (1995; Zbl 0831.58026)], one can define a smooth function, called the function \textit{epsilon}, which is the main object of the theory. The first explicit calculation of this function appears in \textit{J. H. Rawnsley}, Q. J. Math., Oxf. II. Ser. 28, 403-415 (1977; Zbl 0387.58002). In the present paper, the function epsilon is computed for the case of complex tori and Riemann surfaces.