Dynamical Zeta Function for Several Strictly Convex Obstacles
نویسندگان
چکیده
The behavior of the dynamical zeta function ZD(s) related to several strictly convex disjoint obstacles is similar to that of the inverse Q(s) = 1 ζ(s) of the Riemann zeta function ζ(s). Let Π(s) be the series obtained from ZD(s) summing only over primitive periodic rays. In this paper we examine the analytic singularities of ZD(s) and Π(s) close to the line Rs = s2, where s2 is the abscissa of absolute convergence of the series obtained by the second iterations of the primitive periodic rays. We show that at least one of the functions ZD(s), Π(s) has a singularity at s = s2.
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