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Probing gluon number fluctuation effects in future electron-hadron colliders

The description of the QCD dynamics in the kinematical range which will be probed in the future electron - hadron colliders is still an open question. Although phenomenological studies indicate that the gluon number fluctuations, which are related to discreteness in the QCD evolution, are negligible at HERA, the magnitude of these effects for the next generation of colliders still should be estimated. In this paper we investigate inclusive and diffractive $ep$ observables considering a model for the physical scattering amplitude which describes the HERA data. Moreover, we estimate, for the first time, the contribution of the fluctuation effects for the nuclear structure functions. Our results indicate that the study of these observables in the future colliders can be useful to constrain the presence of gluon number fluctuations.