Abstract
General properties of a meromorphic approximation of a scattering amplitude are investigated. The case of an amplitude with nou-channel poles and real, equally spaced,s-channel poles is considered. This amplitude is required to behave as a power ofs ass → ∞ outside the positive real axis. This determines the main features of the distribution of itss-channel zeros. Furthermore, if these zeros satisfy suitable uniformity conditions as functions oft, one finds that the exponent ofs appearing in thes-channel asymptotic behaviour cannot be an arbitrary function oft. This results from the polynomial character of the residues at thes-channel poles. In particular, if this exponent is assumed to be an entire function oft, it must be a linear function oft. Thus, the leadingt-channel poles have to be on a linear trajectory and thes-channel asymptotic behaviour has to be the Regge behaviour associated with this trajectory.
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