We study an importance of the longitudinally polarized virtual photons \gamma * _L in the semi-inclusive ep processes in the ep center-of-mass and Breit frames, and for various distributions. We used the factorization formulae for the unpolarized inclusive and semi-inclusive ep processes which hold in an arbitrary reference frame. The numerical studies were performed for the ep HERA collider for a process with a large-p_T (prompt) photons production, i.e. , the unpolarized Compton process e p \rightarrow e \gamma X, in the Born approximation. In the ep center-of-mass frame we found that the differential cross section for the longitudinally polarized intermediate photon, d \sigma _L, and the term due to the interference between the longitudinal- and transverse-polarization states of the photon, d \tau _LT, are small, i.e. below 10 \% of the cross section. Moreover, these two contributions almost cancel one another, leading to a stronger domination of the transversely polarized virtual photon, even for its large virtuality Q². We found that in this frame the interference term gives non-vanishing contributions even for the cross sections integrated over the azimuthal angle, contrary to a naive expectation. Relevance of the contributions of the longitudinal photon in a jet production in DIS events at the HERA collider is commented. A relatively large (\sim 30 \%) effect due to the interference term d \tau _LT was found for the considered process at the HERA collider in the azimuthal-angle distribution in the Breit frame. Here this contribution vanishes in the cross section integrated over \phi .

PACS numbers: 13.60.Fz, 12.38.Bx, 14.70.Bh